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 = 1
0

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
      
This fraction may be reduced by canceling the common factor of 2 from numerator and denominator to obtain

      

24.