Wednesday, December 3, 2008
Math and Technology
One of the big questions in math education today is: how should we use technology in the classroom? Today I want to explore that question with you. The link to the right is an equation solver; it will show you all the steps and the solution to any equation. Your challenge today is to pick any five equations from the list and use the solver to find an answer. Copy the complete answers to a word document and email them to me. On the comment line answer the following question: Do you think it is better to use paper and pencil to solve an equation or use technology. Explain your position.
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11 comments:
#8 Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
#12Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
#8 Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
#12Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
Jose j. Montanez
2. Simplifying
3h + -5h + 11 = 17
Reorder the terms:
11 + 3h + -5h = 17
Combine like terms: 3h + -5h = -2h
11 + -2h = 17
Solving
11 + -2h = 17
Solving for variable 'h'.
Move all terms containing h to the left, all other terms to the right.
Add '-11' to each side of the equation.
11 + -11 + -2h = 17 + -11
Combine like terms: 11 + -11 = 0
0 + -2h = 17 + -11
-2h = 17 + -11
Combine like terms: 17 + -11 = 6
-2h = 6
Divide each side by '-2'.
h = -3
Simplifying
h = -3
3. Simplifying
2t + 8 + -1t = -3
Reorder the terms:
8 + 2t + -1t = -3
Combine like terms: 2t + -1t = 1t
8 + 1t = -3
Solving
8 + 1t = -3
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + 1t = -3 + -8
Combine like terms: 8 + -8 = 0
0 + 1t = -3 + -8
1t = -3 + -8
Combine like terms: -3 + -8 = -11
1t = -11
Divide each side by '1'.
t = -11
Simplifying
t = -11
5. Simplifying
3c + -8c + 7 = -18
Reorder the terms:
7 + 3c + -8c = -18
Combine like terms: 3c + -8c = -5c
7 + -5c = -18
Solving
7 + -5c = -18
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -5c = -18 + -7
Combine like terms: 7 + -7 = 0
0 + -5c = -18 + -7
-5c = -18 + -7
Combine like terms: -18 + -7 = -25
-5c = -25
Divide each side by '-5'.
c = 5
Simplifying
c = 5
6. Simplifying
7g + 14 + -5g = -8
Reorder the terms:
14 + 7g + -5g = -8
Combine like terms: 7g + -5g = 2g
14 + 2g = -8
Solving
14 + 2g = -8
Solving for variable 'g'.
Move all terms containing g to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + 2g = -8 + -14
Combine like terms: 14 + -14 = 0
0 + 2g = -8 + -14
2g = -8 + -14
Combine like terms: -8 + -14 = -22
2g = -22
Divide each side by '2'.
g = -11
Simplifying
g = -11
8. Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
9. Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
11. Simplifying
5(3x + 12) = -15
Reorder the terms:
5(12 + 3x) = -15
(12 * 5 + 3x * 5) = -15
(60 + 15x) = -15
Solving
60 + 15x = -15
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-60' to each side of the equation.
60 + -60 + 15x = -15 + -60
Combine like terms: 60 + -60 = 0
0 + 15x = -15 + -60
15x = -15 + -60
Combine like terms: -15 + -60 = -75
15x = -75
Divide each side by '15'.
x = -5
Simplifying
x = -5
12. Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
14. Simplifying
-4x + 3(2x + -5) = 31
Reorder the terms:
-4x + 3(-5 + 2x) = 31
-4x + (-5 * 3 + 2x * 3) = 31
-4x + (-15 + 6x) = 31
Reorder the terms:
-15 + -4x + 6x = 31
Combine like terms: -4x + 6x = 2x
-15 + 2x = 31
Solving
-15 + 2x = 31
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + 2x = 31 + 15
Combine like terms: -15 + 15 = 0
0 + 2x = 31 + 15
2x = 31 + 15
Combine like terms: 31 + 15 = 46
2x = 46
Divide each side by '2'.
x = 23
Simplifying
x = 23
15. Simplifying
3(t + -12) = 27
Reorder the terms:
3(-12 + t) = 27
(-12 * 3 + t * 3) = 27
(-36 + 3t) = 27
Solving
-36 + 3t = 27
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '36' to each side of the equation.
-36 + 36 + 3t = 27 + 36
Combine like terms: -36 + 36 = 0
0 + 3t = 27 + 36
3t = 27 + 36
Combine like terms: 27 + 36 = 63
3t = 63
Divide each side by '3'.
t = 21
Simplifying
t = 21
17. Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
18. Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
#8 Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
kevin
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
#12Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
#8 Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
#12Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
kevin s.
Simplifying
3h + -5h + 11 = 17
Reorder the terms:
11 + 3h + -5h = 17
Combine like terms: 3h + -5h = -2h
11 + -2h = 17
Solving
11 + -2h = 17
Solving for variable 'h'.
Move all terms containing h to the left, all other terms to the right.
Add '-11' to each side of the equation.
11 + -11 + -2h = 17 + -11
Combine like terms: 11 + -11 = 0
0 + -2h = 17 + -11
-2h = 17 + -11
Combine like terms: 17 + -11 = 6
-2h = 6
Divide each side by '-2'.
h = -3
Simplifying
h = -3
Simplifying
2t + 8 + -1t = -3
Reorder the terms:
8 + 2t + -1t = -3
Combine like terms: 2t + -1t = 1t
8 + 1t = -3
Solving
8 + 1t = -3
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + 1t = -3 + -8
Combine like terms: 8 + -8 = 0
0 + 1t = -3 + -8
1t = -3 + -8
Combine like terms: -3 + -8 = -11
1t = -11
Divide each side by '1'.
t = -11
Simplifying
t = -11
Simplifying
3c + -8c + 7 = -18
Reorder the terms:
7 + 3c + -8c = -18
Combine like terms: 3c + -8c = -5c
7 + -5c = -18
Solving
7 + -5c = -18
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -5c = -18 + -7
Combine like terms: 7 + -7 = 0
0 + -5c = -18 + -7
-5c = -18 + -7
Combine like terms: -18 + -7 = -25
-5c = -25
Divide each side by '-5'.
c = 5
Simplifying
c = 5
Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
Simplifying
7G + 14 + -5G = -8
Reorder the terms:
14 + 7G + -5G = -8
Combine like terms: 7G + -5G = 2G
14 + 2G = -8
Solving
14 + 2G = -8
Solving for variable 'G'.
Move all terms containing G to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + 2G = -8 + -14
Combine like terms: 14 + -14 = 0
0 + 2G = -8 + -14
2G = -8 + -14
Combine like terms: -8 + -14 = -22
2G = -22
Divide each side by '2'.
G = -11
Simplifying
G = -11
Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
Simplifying
5(3x + 12) = -15
Reorder the terms:
5(12 + 3x) = -15
(12 * 5 + 3x * 5) = -15
(60 + 15x) = -15
Solving
60 + 15x = -15
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-60' to each side of the equation.
60 + -60 + 15x = -15 + -60
Combine like terms: 60 + -60 = 0
0 + 15x = -15 + -60
15x = -15 + -60
Combine like terms: -15 + -60 = -75
15x = -75
Divide each side by '15'.
x = -5
Simplifying
x = -5
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
-4x + 3(2x + -5) = 31
Reorder the terms:
-4x + 3(-5 + 2x) = 31
-4x + (-5 * 3 + 2x * 3) = 31
-4x + (-15 + 6x) = 31
Reorder the terms:
-15 + -4x + 6x = 31
Combine like terms: -4x + 6x = 2x
-15 + 2x = 31
Solving
-15 + 2x = 31
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + 2x = 31 + 15
Combine like terms: -15 + 15 = 0
0 + 2x = 31 + 15
2x = 31 + 15
Combine like terms: 31 + 15 = 46
2x = 46
Divide each side by '2'.
x = 23
Simplifying
x = 23
Simplifying
3 + (t + -12) = 27
Reorder the terms:
3 + (-12 + t) = 27
Remove parenthesis around (-12 + t)
3 + -12 + t = 27
Combine like terms: 3 + -12 = -9
-9 + t = 27
Solving
-9 + t = 27
Solving for variable 't'.
Move all terms containing t to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + t = 27 + 9
Combine like terms: -9 + 9 = 0
0 + t = 27 + 9
t = 27 + 9
Combine like terms: 27 + 9 = 36
t = 36
Simplifying
t = 36
Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
Simplifying
3c + -8c + 7 = -8
Reorder the terms:
7 + 3c + -8c = -8
Combine like terms: 3c + -8c = -5c
7 + -5c = -8
Solving
7 + -5c = -8
Move all terms containing c to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -5c = -8 + -7
Combine like terms: 7 + -7 = 0
0 + -5c = -8 + -7
-5c = -8 + -7
Combine like terms: -8 + -7 = -15
-5c = -15
Divide each side by '-5'.
c = 3
Simplifying
c = 3
Simplifying
7g + 14 + -5g = -8
Reorder the terms:
14 + 7g + -5g = -8
Combine like terms: 7g + -5g = 2g
14 + 2g = -8
Solving
14 + 2g = -8
Move all terms containing g to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + 2g = -8 + -14
Combine like terms: 14 + -14 = 0
0 + 2g = -8 + -14
2g = -8 + -14
Combine like terms: -8 + -14 = -22
2g = -22
Divide each side by '2'.
g = -11
Simplifying
g = -11
Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
5(3x + 12) = -15
Reorder the terms:
5(12 + 3x) = -15
(12 * 5 + 3x * 5) = -15
(60 + 15x) = -15
Solving
60 + 15x = -15
Move all terms containing x to the left, all other terms to the right.
Add '-60' to each side of the equation.
60 + -60 + 15x = -15 + -60
Combine like terms: 60 + -60 = 0
0 + 15x = -15 + -60
15x = -15 + -60
Combine like terms: -15 + -60 = -75
15x = -75
Divide each side by '15'.
x = -5
Simplifying
x = -5
Simplifying
3h + -5h + 11 = 17
Reorder the terms:
11 + 3h + -5h = 17
Combine like terms: 3h + -5h = -2h
11 + -2h = 17
Solving
11 + -2h = 17-4x + 3(2x + -5) = 31
Reorder the terms:
-4x + 3(-5 + 2x) = 31
-4x + (-5 * 3 + 2x * 3) = 31
-4x + (-15 + 6x) = 31
Reorder the terms:
-15 + -4x + 6x = 31
Combine like terms: -4x + 6x = 2x
-15 + 2x = 31
Solving
-15 + 2x = 31
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + 2x = 31 + 15
Combine like terms: -15 + 15 = 0
0 + 2x = 31 + 15
2x = 31 + 15
Combine like terms: 31 + 15 = 46
2x = 46
Divide each side by '2'.
x = 23
Simplifying
x = 23
Solving for variable 'h'.
Move all terms containing h to the left, all other terms to the right.
Add '-11' to each side of the equation.
11 + -11 + -2h = 17 + -11
Combine like terms: 11 + -11 = 0
0 + -2h = 17 + -11
-2h = 17 + -11
Combine like terms: 17 + -11 = 6
-2h = 6
Divide each side by '-2'.
h = -3
Simplifying
h = -3
3c + -8c + 7 = -18
Reorder the terms:
7 + 3c + -8c = -18
Combine like terms: 3c + -8c = -5c
7 + -5c = -18
Solving
7 + -5c = -18
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -5c = -18 + -7
Combine like terms: 7 + -7 = 0
0 + -5c = -18 + -7
-5c = -18 + -7
Combine like terms: -18 + -7 = -25
-5c = -25
Divide each side by '-5'.
c = 5
Simplifying
c = 52(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 35(3x + 12) = -15
Reorder the terms:
5(12 + 3x) = -15
(12 * 5 + 3x * 5) = -15
(60 + 15x) = -15
Solving
60 + 15x = -15
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-60' to each side of the equation.
60 + -60 + 15x = -15 + -60
Combine like terms: 60 + -60 = 0
0 + 15x = -15 + -60
15x = -15 + -60
Combine like terms: -15 + -60 = -75
15x = -75
Divide each side by '15'.
x = -5
Simplifying
x = -5
#8 Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
#12Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
zarina 12/3/08
#8 Simplifying
2(a + -4) + 15 = 13
Reorder the terms:
2(-4 + a) + 15 = 13
(-4 * 2 + a * 2) + 15 = 13
(-8 + 2a) + 15 = 13
Reorder the terms:
-8 + 15 + 2a = 13
Combine like terms: -8 + 15 = 7
7 + 2a = 13
Solving
7 + 2a = 13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 2a = 13 + -7
Combine like terms: 7 + -7 = 0
0 + 2a = 13 + -7
2a = 13 + -7
Combine like terms: 13 + -7 = 6
2a = 6
Divide each side by '2'.
a = 3
Simplifying
a = 3
#12Simplifying
4(2a + 2) + -17 = 15
Reorder the terms:
4(2 + 2a) + -17 = 15
(2 * 4 + 2a * 4) + -17 = 15
(8 + 8a) + -17 = 15
Reorder the terms:
8 + -17 + 8a = 15
Combine like terms: 8 + -17 = -9
-9 + 8a = 15
Solving
-9 + 8a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 8a = 15 + 9
Combine like terms: -9 + 9 = 0
0 + 8a = 15 + 9
8a = 15 + 9
Combine like terms: 15 + 9 = 24
8a = 24
Divide each side by '8'.
a = 3
Simplifying
a = 3
Simplifying
7 + 2(a + -3) = -9
Reorder the terms:
7 + 2(-3 + a) = -9
7 + (-3 * 2 + a * 2) = -9
7 + (-6 + 2a) = -9
Combine like terms: 7 + -6 = 1
1 + 2a = -9
Solving
1 + 2a = -9
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + 2a = -9 + -1
Combine like terms: 1 + -1 = 0
0 + 2a = -9 + -1
2a = -9 + -1
Combine like terms: -9 + -1 = -10
2a = -10
Divide each side by '2'.
a = -5
Simplifying
a = -5
Simplifying
2(3a + 2) = -8
Reorder the terms:
2(2 + 3a) = -8
(2 * 2 + 3a * 2) = -8
(4 + 6a) = -8
Solving
4 + 6a = -8
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 6a = -8 + -4
Combine like terms: 4 + -4 = 0
0 + 6a = -8 + -4
6a = -8 + -4
Combine like terms: -8 + -4 = -12
6a = -12
Divide each side by '6'.
a = -2
Simplifying
a = -2
Simplifying
5(b + 4) + -6b = -24
Reorder the terms:
5(4 + b) + -6b = -24
(4 * 5 + b * 5) + -6b = -24
(20 + 5b) + -6b = -24
Combine like terms: 5b + -6b = -1b
20 + -1b = -24
Solving
20 + -1b = -24
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-20' to each side of the equation.
20 + -20 + -1b = -24 + -20
Combine like terms: 20 + -20 = 0
0 + -1b = -24 + -20
-1b = -24 + -20
Combine like terms: -24 + -20 = -44
-1b = -44
Divide each side by '-1'.
b = 44
Simplifying
b = 44
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