1. Unit 3 -
Homework 4
Solving Equations with Variables on Both Sides

2. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.

3. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.
(2) Combine all like terms on each side of the equal sign.

4. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.
(2) Combine all like terms on each side of the equal sign.
★ Same Side, Same Operation

5. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.
(2) Combine all like terms on each side of the equal sign.
★ Same Side, Same Operation
(3) Get variables to one side of =. Moving the smallest
will avoid dividing by a negative.

6. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.
(2) Combine all like terms on each side of the equal sign.
★ Same Side, Same Operation
(3) Get variables to one side of =. Moving the smallest
will avoid dividing by a negative.
★ Opposite Side, Opposite Operation

7. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.
(2) Combine all like terms on each side of the equal sign.
★ Same Side, Same Operation
(3) Get variables to one side of =. Moving the smallest
will avoid dividing by a negative.
★ Opposite Side, Opposite Operation
(4) Isolate term with variable.

8. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.
(2) Combine all like terms on each side of the equal sign.
★ Same Side, Same Operation
(3) Get variables to one side of =. Moving the smallest
will avoid dividing by a negative.
★ Opposite Side, Opposite Operation
(4) Isolate term with variable.
★ Opposite Side, Opposite Operation

9. Steps to Solve Equations
with Variables on Both Sides
(1) Take care of any parenthesis by distributing.
(2) Combine all like terms on each side of the equal sign.
★ Same Side, Same Operation
(3) Get variables to one side of =. Moving the smallest
will avoid dividing by a negative.
★ Opposite Side, Opposite Operation
(4) Isolate term with variable.
★ Opposite Side, Opposite Operation
(5) Multiply or Divide to get coefficient of variable to 1.

10. Solve: 2a − 3 = 5a − 8

11. Solve: 2a − 3 = 5a − 8
✦ Variables together
Opposite side =
Opposite operation

12. Solve: 2a − 3 = 5a − 8
✦ Variables together
Opposite side =
Opposite operation
✦ Moving the smallest
avoids dividing by a
negative.

13. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation
✦ Moving the smallest
avoids dividing by a
negative.

14. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest
avoids dividing by a
negative.

15. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest
avoids dividing by a
negative.
✦ Isolate variable term.

16. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest
avoids dividing by a
negative.
✦ Isolate variable term.

17. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest +8 +8
avoids dividing by a
negative.
✦ Isolate variable term.

18. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest +8 +8
avoids dividing by a
negative.
5 = 3a
✦ Isolate variable term.

19. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest +8 +8
avoids dividing by a
negative.
5 = 3a
✦ Isolate variable term.
✦ Divide by variables
coefficient to make
coefficient of variable 1.

20. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest +8 +8
avoids dividing by a
negative.
5 = 3a
Isolate variable term.
3 3
✦
✦ Divide by variables
coefficient to make
coefficient of variable 1.

21. Solve: 2a − 3 = 5a − 8
✦ Variables together −2a −2a
Opposite side =
Opposite operation −3 = 3a − 8
✦ Moving the smallest +8 +8
avoids dividing by a
negative.
5 = 3a
Isolate variable term.
3 3
✦
✦ Divide by variables
coefficient to make 5
coefficient of variable 1. =a
3

22. Solve: −3( x − 2 ) = −7 ( x + 5 )

23. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute.

24. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35

25. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together,
moving smallest.
Opposite side =
Opposite operation

26. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side =
Opposite operation

27. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation

28. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation
✦ Isolate variable term.

29. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation
✦ Isolate variable term.

30. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation −6 −6
✦ Isolate variable term.

31. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation −6 −6
✦ Isolate variable term. 4x = −41

32. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation −6 −6
✦ Isolate variable term. 4x = −41
✦ Divide to make
coefficient of variable 1.

33. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation −6 −6
✦ Isolate variable term. 4x = −41
✦ Divide to make 4 4
coefficient of variable 1.

34. Solve: −3( x − 2 ) = −7 ( x + 5 )
✦ Distribute. −3x + 6 = −7x − 35
✦ Variables together, +7x +7x
moving smallest.
Opposite side = 4x + 6 = −35
Opposite operation −6 −6
✦ Isolate variable term. 4x = −41
✦ Divide to make 4 4
coefficient of variable 1.
41
x=−
4

35. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)

36. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute.

37. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3

38. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on
left side.

39. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side.

40. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side.
✦ Variables together,
moving smallest.
Opposite side =
Opposite operation

41. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest.
Opposite side =
Opposite operation

42. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side =
Opposite operation

43. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side =
Opposite operation
✦ Isolate variable term.

44. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side =
Opposite operation
✦ Isolate variable term.

45. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side = −22 −22
Opposite operation
✦ Isolate variable term.

46. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side = −22 −22
Opposite operation
19x = −19
✦ Isolate variable term.

47. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side = −22 −22
Opposite operation
19x = −19
✦ Isolate variable term.
✦ Divide to make
coefficient of variable 1.

48. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side = −22 −22
Opposite operation
19x = −19
✦ Isolate variable term.
19 19
✦ Divide to make
coefficient of variable 1.

49. Solve: 9 ( 2x + 3) − 5 = − ( x − 3)
✦ Distribute. 18x + 27 − 5 = −x + 3
✦ Combine like terms on 18x + 22 = −x + 3
left side. +1x +1x
✦ Variables together,
moving smallest. 19x + 22 = 3
Opposite side = −22 −22
Opposite operation
19x = −19
✦ Isolate variable term.
19 19
✦ Divide to make
coefficient of variable 1. x = −1