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MATH
140 -- Intermediate Algebra -- Exercise Solutions
Section: 2.1
2.
Solve 8x = - 40
Solution:
8x
= - 40
Divide
both sides of the equation by 8
x
= - 5
4. Solve
y - 8.6 = - 6.3
Solution:
y
- 8.6 = - 6.3
Add
8.6 to both sides of the equation
y
= 2.3
6.
Solve
2y - 3= 11
Solution:
2y
- 3= 11
Add
3 to both sides of the equation
2y
= 14
Divide
both sides of the equation by 2
y = 7
8.
Solve
- 9 = 5x + 11
Solution:
-
9 = 5x + 11
Add
-11 to both sides of the equation
-
20 = 5x
Divide
both sides of the equation by 5
- 4 = x
10.
Solve
10.3 - 6x = - 2.3
Solution:
10.3
- 6x = - 2.3
Add
-10.3 to both sides of the equation
-
6x = - 12.6
Divide
both sides of the equation by - 6
x = - 2.1
12.
Solve
4x + 14 = 6x + 8
Solution:
4x
+ 14 = 6x + 8
Add
-14 to both sides of the equation
4x
= 6x - 6
Add
- 6x to both sides of the equation
-2x
= - 6
Divide
both sides of the equation by - 2
x = 3
14.
Solve
6 + 3x + x = - x + 2 - 26
Solution:
6
+ 3x + x = - x + 2 - 26
Combine
like terms
6
+ 4x = -x - 24
Add
- 6 to both sides of the equation
4x
= - x - 30
Add
x to both sides of the equation
5x
= - 30
Divide
both sides of the equation by 5
x = - 6
16.
Solve
2 (x + 3) = x + 5
Solution:
2
(x + 3) = x + 5
Use
the Distributive Law to remove parenthesis
2x
+ 6 = x + 5
Add
- 6 to both sides of the equation
2x
= x - 1
Add
- x to both sides of the equation
x
= - 1
18.
Solve
6x = 4(5 + x)
Solution:
6x
= 4(5 + x)
Use
the Distributive Law to remove parenthesis
6x
= 20 + 4x
Add
- 4x to both sides of the equation
2x
= 20
Divide
both sides of the equation by 2
x
= 10
20.
Solve
- 3(2w - 7) - 10 = 9 - 2(5w + 4)
Solution:
-
3(2w - 7) - 10 = 9 - 2(5w + 4)
Use
the Distributive Law to remove parenthesis
-
6w + 21 - 10 = 9 - 10w - 8
Add
10w to both sides of the equation
4w
+ 21 - 10 = 9 - 8
Add
the numerical constants
4w
+ 11 = 1
Add
-11 to both sides of the equation
4w
= -10
Divide
both sides of the equation by 4
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This
fraction may be reduced by canceling the common factor of 2 from numerator and
denominator to obtain
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24.
