1. Learn how to solve mutli-step equations…
Solving Equations
Learn how to solve mutli-step equations…

2. The End Goal
To get the variable by it’s self!!!!!

3. One Variable / Two Operations

4. 2x + 5 = 15 : Solve of x 2x = 15 – 5 2x = 10 X = 10/2 X = 5 Check:
Move items away from the term containing the variable
Move items to get variable alone
2x = 15 – 5
2x = 10
X = 10/2
X = 5
Check:
? x = 5 ?
2(5) + 5
10 + 5 15
15 = 15
Correct!

5. 10a - 4 = 26 : Solve of a 10a = 26 + 4 10a = 30 a = 30/10 a = 3 Check:
Move items away from the term containing the variable
Move items to get variable alone
10a =
10a = 30
a = 30/10
a = 3
Check:
? a = 3 ?
10(3) - 4
30 - 4 26
26 = 26
Correct!

6. h/4 + 8 = - 4 : Solve of h h/4 = - 4 - 8 h/4 = - 12 h = -12 x 4
Move items away from the term containing the variable
Move items to get variable alone
h/4 =
h/4 = - 12
h = -12 x 4
h = - 48
Check:
? h = - 48 ?
- 48/4 + 8
- 4
- 4 = - 4
Correct!

7. m/3 - 2 = 10 : Solve of h m/3 = 10 + 2 m/3 = 12 m = 12 x 3 m = 36
Move items away from the term containing the variable
Move items to get variable alone
m/3 =
m/3 = 12
m = 12 x 3
m = 36
Check:
? m = 36 ?
36/3 - 2
12 - 2 10
10 = 10
Correct!

8. Two Variables
One on each side

9. 13x – 5 = 10x + 7 : Solve for x 13x -10x – 5 = 7 3x – 5 = 7 3x = 7 + 5
1st: Get x’s on the same side
Move all items without the variable to other side
Get x alone
13x -10x – 5 = 7
3x – 5 = 7
3x = 7 + 5
3x = 12
X = 12/3
X = 4

10. j + 6 = 2j – 8: Solve for j j – 2j + 6 = - 8 - j + 6 = - 8
1st: Get x’s on the same side
Move all items without the variable to other side
Get j alone
j – 2j + 6 = - 8
- j + 6 = - 8
- j =
- j = - 14
j = - 14/-1
j = 14

11. Distributive One Variable

12. 4(x – 2) = 12 : Solve for x 4x – 8 = 12 4x = 12 + 8 4x = 20 x = 20 / 4
Distribute to everything inside the ( )
Move items away from the term containing the variable
Move items to get variable alone
4x – 8 = 12
4x =
4x = 20
x = 20 / 4
x = 5

13. -2(p + 8) = 4 : Solve for p -2p – 16 = 4 -2p = 4 + 16 -2p = 20
Distribute to everything inside the ( )
Move items away from the term containing the variable
Move items to get variable alone
-2p – 16 = 4
-2p =
-2p = 20
p = 20 / - 2
p = - 10

14. 5(f - 6) = 10 : Solve for f 5f – 30 = 10 5f = 10 + 30 5f = 40
Distribute to everything inside the ( )
Move items away from the term containing the variable
Move items to get variable alone
5f – 30 = 10
5f =
5f = 40
f = 40 / 5
f = 8

15. Distributive With Two Variables
One on each side

16. 6(2x – 5) = 4x + 2: Solve for x 12x – 30 = 4x + 2 12x – 4x - 30 = 2
Distribute everything inside the ( )
1st: Get x’s on the same side
Move all items without the variable to other side
Get x alone
12x – 30 = 4x + 2
12x – 4x - 30 = 2
8x - 30= 2
8x =
8x = 32
x = 32/4
x = 4

17. 2(4x + 6) = 3x - 13: Solve for x 8x + 12 = 3x - 9 8x – 3x + 12 = - 13
Distribute everything inside the ( )
1st: Get x’s on the same side
Move all items without the variable to other side
Get x alone
8x + 12 = 3x - 9
8x – 3x + 12 = - 13
5x + 12 = - 13
5x =
5x = -25
x = -25/5
x = -5

18. Distributive With Many Variables
Several variables on each side

19. 8x – 3(x – 1) = 4(x + 2) : Solve for x
Distribute to get rid of all ( )
Put x terms together
Get x terms on the same side
Move all items away from the x term
8x – 3x + 3 = 4(x + 2)
8x – 3x + 3 = 4x + 8
5x + 3 = 4x + 8
5x – 4x + 3 = 8
x + 3 = 8
x = 8 – 3
x = 5

20. 14 – (6x – 5) = 5(2x – 1) – 4x : Solve for x
Distribute to get rid of all ( )
Put x terms together & other like terms
Get x terms on the same side
Move all items away from the x term
Get x alone
14 – 6x + 5 = 5(2x -1)
14 – 6x + 5 = 10x – 5 – 4x
-6x + 19= 10x – 5 – 4x
-6x + 19 = 6x - 5
-6x – 6x + 19 = -5
-12x + 19 = -5
-12x = -5 – 19
-12x = -24
x = -24 / -12
x = 2