Solving Multi-Step Equations

Check this answer (and every answer on this test) on the next slide.

1) When there is a number or variable right next to a

parenthesis without an operational sign, it is understood

to be multiplication.  Therefore, we have to multiply

that number or variable by everything inside the

parentheses. 

Ex:  3(x + 4) = 3x + 12

       4(2x - 3) = 8x - 12

       -(x + 3)  =  -x - 3

 

What would 4(x + 5) equal?

4x + 5
4x - 5
4x + 20
4x - 20

Answer to previous question:

4(x + 5) =


4x + 4•5


4x + 20




When there is a number or variable right next to a

parenthesis without an operational sign, it is understood

to be multiplication.  Therefore, we have to multiply

that number or variable by everything inside the

parentheses. 

Ex:  3(x + 4) = 3x + 12

       4(2x - 3) = 8x - 12

       -(x + 3)  =  -x - 3

 

6x + 12
6x - 12

2)  What would 3(2x + 4) equal?

3x + 4
2x + 12

Answer to previous question: 

3(2x + 4) =


32x + 3•4


6x +12

 

 

 


3)  What would 3(2x - 4) equal?

6x + 12
6x - 12
3x + 4
2x + 12

Answer to previous question:  3(2x -4) = 6x - 12

 

 

 

 

 

 

4)  What would 3(-x - 4) equal?

6x + 12
6x - 12
-3x - 12
2x + 12

Answer to previous question:  3(-x - 4) = -3x - 12

 

 

 

 

 

 

5)  What would -3(-x - 4) equal?

6x + 12
6x - 12
-3x - 4
3x + 12

Answer to previous:  -3(-x -4) = 3x + 12

 

3x + 4x = 21 has variables on the same side of the

equal side.  They can be combined to make 7x = 21. 

 

Where 3x = 4x + 21  variables on different sides. 

-4x needs to be added to both sides to clear it from 

the side with the number so that variables are on one

side and the numbers are on the other side.

 

6) On 5 = 2x + 3x what needs to be done first?

2x + 3x can be combined to make 5 = 5x

-2x can be added to both sides to make 5 - 2x = 3x

Previous answer: 2x + 3x is combined to make  5x.

 

 

We combine like variables or numbers on the same side

on an equation following the signs.  We move variables

 or numbers to the other side by adding their opposites

to both sides.

 

 

 

Combine like terms

7) On 5 - 2x = 3x what needs to be done first?

 

 

Move variables to one side and numbers to the other

Answer to previous question: 

5 - 2x = 3x

   +2x   +2x

5         = 5x    "Move variables to one side"

5            5

        x =  1 

 

Combine like terms

Move variables to one side and numbers to the other

  

8) On 4x = 3x - 9 what needs to be done first?

Answer to previous question: 

   4x = 3x - 9   "Move variables to one side"

 -3x  -3x

     x = -9


 

Combine like terms

Move variables to one side and numbers to the other


9) On 4x + 3x = 21 what needs to be done first?

 

Combine like terms

Answer to previous question: 

On 4x + 3x = 21 what needs to be done first?

Combine like terms  4x + 3x to get 7x

7x = 21

7      7

x     =  3

 

 

10)What needs to be done first on 3x + 5 - 8 = 9?

Move variables to one side and numbers to the other

Combine like terms

Move variables to one side and numbers to the other

Answer to previous question: 

What needs to be done first on 3x + 5 - 8 = 9?

 

Combine like terms + 5 - 8 to get -3

3x -3 = 9    Then move numbers to one side

     +3  +3         by adding the opposite of -3

3x      = 12

 3           3   Now clear multiplication with division

  x      =  4



11) What needs to be done first on 2x - 4 = 9?

 6

Answer to previous question: 

What needs to be done first on 2x - 4 = 9?

Move variables to one side and numbers to the other by

adding the opposite of -4 to both sides.

2x -4 = 9

     +4  +4

2x = 13

 2      2

x = 6.5 or 6 1/2 or 13/2




12) Solve:  2x = -3x + 30

 5

 -5

 -6

Answer to previous question: 

Solve  2x = -3x + 30

         +3x   +3x               to move variables to one side

            5x    =        30

             5                5   to undo multiplication

              x     =       6

 

 

 

 

13) Solve:  3x + 7 = 2x + 2

-3

 5

 -5

 3

-3

Answer to previous question: 

Solve  3x + 7 = 2x + 2     Move variables to one side

         -2x          -2x               by -2x from both sides

           x   +7   =    2         Move numbers to other       

                -7        -7 

 

           x         =   -5

 

 

14) Solve:  2(x + 3) = -4x - 12

 5

 -5

3

Distribute

Answer to previous question: 

Solve: 2(x + 3) = -4x - 12   Distribute 2 first

            2x + 6  = -4x - 12           

            +4x         +4x          Move variables to one side

                                              

            6x  + 6  =         -12  Numbers to the other side

                   -6          -6

           6x            =  -18        Clear multiplication with division 

        

What operation was the final step?
6
x = -3
6

Move variables

Division

Answer to previous question: 

1st Step:  Distribute

2nd Step:  Combine any like terms on the same side

3rd Step:  Variables to one side

4th Step:  Numbers to the other side

5th Step:  Clear multiplication or division w/inverse

 

 

 

16) Solve:        + 5 = 3

  6

3

  -6

-2

-2

Answer to previous question: 

 

Solve:        + 5 = 3           -5 to both sides

                  -5    -5

 

                       =  -2          Multiply both sides by 3 

                   

 x =   -6


 

17) Solve:           + 4 =    8   

  8

3 *

3

3

-2

 -24

x
* 3

-8

24

 20

18)             - 4  = -8

Answer to previous question: 

 

Solve:        + 4 = 8     -4 to both sides

    

                   -4    -4

 

                         =  4                Multiply both sides by -2                         

            


x  =  -8

 

 

-2 •

-2

-2

-5

x

 -24

• -2

 -20

24

 60

Answer to previous question:

 

Solve:        - 4 = -8     +4 to both sides

               

                 +4    +4

 

                         =  -4          Multiply both sides by -5 

 

            x  =   20

 

 

19) Solve:          + 4 =    -8

-5 *

-5

-5

-5

 -24

x
* -5

 -60

24

 60

Answer to previous question: 

 

 

Solve:        + 4 = -8               Add -4 to both sides

                    -4    -4

 

                      =  -12           Multiply both sides by -5  

               

                 x  =   60

 

20)  Solve:    -      x  + 3 =    7

 

-5 *

-5

-5

 -24

1

6

* -5

 -60

24

 -33

Answer to previous question: 

Solve: -     x + 3 = 7             Add -3 to both sides

                    -3    -3

 

               x       =  4

                                          we can not divide fractions

                x  =   -24          multiply by the reciprocal

 

 

 

21)  Solve:         x  +  3  =  -8

-6 *

6

1

 6

1

 -2

3

1

* -6

 33

2

 6

Answer to previous question: 

 

Solve:       x + 3 = -8     -3 to both sides to move #'s

                    -3    -3

 

               x       =  -11            Multiply by the reciprocal

                                                 

                    x  =   -33  

            

 

 

 

22) Solve:        x  + 3 =    7

3 *

 3

1

3

1

3

2

 -6

* 3

9

-9

Answer to previous question: 

 

Solve:       x + 3 = 7     -3 to both sides to move #'s

                    -3    -3

 

               x       =  4               Multiply by the reciprocal

                                                 

                    x  =   6      

 

 

 

23) Solve:        (x -6) = 2

 6

3 *

2

 3

3

2

2

2

3

 -6

* 3

2

9

-9

 10

Answer to previous question:

 

Solve:           (x - 6) = 2          Multiply by the reciprocal

 

                     x - 6 = 3

                        +6  +6       Numbers to other side

                      x   =   9 

 

 

24)  Solve:  4(x + 3) = x - 18

2

3 *

 3

2

 -10

* 3

2

9

-9

Answer to previous question: 

24)  Solve:  4(x + 3) = x - 18    Distribute first.

                      4x + 12 = x -18   Variables to one side

                      -x            -x

                   3x   + 12      =    -18

                           -12             -12   Numbers to other

                   3x               =    -30    Divide by 3

                   3                           3

                     x              =     -10

25) How do we clear division?

By adding

 By subtracting

By multiplying

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