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Algebra Review 2

Solving Linear Equations (Chapter 2)

A.        

1)         2x = 8

            2x ÷2 = 8 ÷2                  ← divided by 2 on both sides

            x = 4

2)         -7y = 35

            -7y ÷ (-7) = 35 ÷ (-7)       ← divided by (-7) on both sides

            y = -5

3)         0.9x = 3.6

            0.9x ÷ 0.9 = 3.6 ÷ 0.9     ← divided by 0.9 on both sides

            x = 4

4)         x + 6 = -2

            x + 6 -6 = -2 -6              ← subtracted 6 on both sides

            x = -8

5)         2x + 7 = x -5

            2x + 7 -x = x -5 -x          ← subtracted x on both sides

            x + 7 = -5

            x + 7 -7 = -5 -7              ← subtracted 7 on both sides

            x = -12  

6)         (2/5)w = 40

            (2/5)w x 5 = 40 x 5         ← multiplied by 5 on both sides

            2w = 200

            2w ÷ 2 = 200 ÷2             ← divided by 2 on both sides

            w = 100

 

 

 

 

B.

7)         7(4x +2) - 54 = 36 - 5(x+2)       

            28x + 14 - 54 = 36 - 5x - 10      ← Break the brackets first

                                                                Recall: a(x + y) = ax + ay

            28x - 40 = 26 - 5x

            28x - 40 + 5x = 26 - 5x + 5x      ← added 5x on both sides

            33x - 40 = 26

            33x - 40 + 40 = 26 + 40             ← added 40 on both sides

            33x = 66                                   ← divided by 33 on both sides

            x = 2

 

 

8)         x + (2/9)x = 22

            (9/9)x + (2/9)x = 22        ← x = 1x where 1 can be expressed as 9/9

            (11/9)x = 22

            (11/9)x  x9 = 22 x9         ← multiplied by 9 on both sides

            11x = 198

11x ÷11= 198 ÷11          ← divided by 11 on both sides

x = 18

 

9)         8(4x -2) - 4(5x +4) -3 = 9x - 10(x-3)         

            32x -16 -20x -16 -3 = 9x -10x +30 ← Break the brackets first

                                                                  Recall: a(x - y) = ax - ay

            12x -35 = -x +30                        ← Group the like terms and simplify

            12x -35 +x = -x +30 +x               ← added x on both sides

            13x -35 = 30

            13x -35 +35 = 30 +35                 ← added 35 on both sides

            13x = 65                                   ← divided by 13 on both sides

            x = 5

 

10)        (1/2)(4x + 8) + (2/3)(6x -3) = (11/3)(9x-6) - 15(x+4)

            2x +4 +4x -2 = 33x -22 -15x -60              ← Break the brackets first

            6x +2 = 18x -82                                     ← Group the like terms and simplify

            6x +2 -6x = 18x -82 -6x                          ← Subtracted 6x on both sides

            2 = 12x -82

            12x -82 = 2

            12x -82 +82 = 2 +82                               ← Added 82 on both sides

            12x = 84                                               ← Divided by 12 on both sides

            x = 7   

 

 

NOTE: You can always check your answer by substituting the x back to the original equation.  Take Question #10 as an example:

LS (left side)      = (1/2)(4x +8) + (2/3)(6x -3)                    

= (1/2)(4(7) +8) + (2/3)(6(7) -3)       ← substitute x = 7 into the equation

                        = (1/2)(36) + (2/3)(39)

                        = 18 +26

                        = 44

RS (right side)   = (11/3)(9x-6) -15(x+4)

                        = (11/3)(9(7)-6) -15(7+4)                ← substitute x = 7 into the equation

                        = (11/3)(57) -15(11)

                        = 209 -165

                        = 44

Since LS = RS, the solution is 7.

 

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