1. Solving Multi-Step Equations
Thinker
Ana has twice as much money as Ben, and Ben has three times as much as Clio. Together they have $190. How much does each person have?
Ana, $114; Ben, $57; Clio, $19

2. COMMON CORE #9B
To solve a multi-step equation, including (1)word problems (2)combining like terms (3)Distributive Property

3. Combining Like Terms Solve 8x + 6 + 3x – 2 = 37
11x + 4 = 37 Combine like terms.
– 4 – 4 Subtract 4 from both sides.
11x = 33 33 11
11x =
Divide both sides by 11.
x = 3

4. Check The Answer!  Check 8x + 6 + 3x – 2 = 37
8(3) (3) – 2 = 37 ?
Substitute 3 for x.
– 2 = 37 ?
37 = 37 ? 

5. You Work This One Solve 6x + 5 + 4x – 13 = 42
10x - 8 = 42 Combine like terms.
Add 8 to both sides.
10x = 50 50 10
10x =
Divide both sides by 10.
x = 5

6. Now Check It  Check 6x + 5 + 4x – 13 = 42 6(5) + 5 + 4(5) – 13 = 42
Substitute 5 for x.
– 13 = 42
42 = 42 

7. Using The Distributive Property
Solve
4(x – 6) + 7 = 11
4(x – 6) + 7 = 11 Distributive Property
4(x) – 4(6) + 7 = 11
Simplify by multiplying:
4(x) = 4x and 4(6) = 24.
4x – = 11
4x – 17 = 11
Simplify by adding: – = 17.
Add 17 to both sides.
4x = 28
Divide both sides by 4. 4
x = 7

8. Now Check It! Check 4(x – 6) + 7 = 11
4(7 – 6) + 7 = 11 Substitute 7 for x
4(1) + 7 = 11
= 11
11 = 11

9. You Try It
Solve
8(x + 2) - 3 = 5
8(x + 2) - 3 = 5 Distributive Property
8(x) + 8(2) - 3 = 5
Simplify by multiplying:
8(x) = 8x and 8(2) =16
8x = 5
8x + 13 = 5
Simplify by adding: = 13
Subtract 13 from both sides.
8x = -8
Divide both sides by 8. 8
x = -1

10. You Check It! Check 8(x + 2) - 3 = 5
8(-1 + 2) - 3 = 5 Subsitute -1 for x
8(1) - 3 = 5
= 5
5 = 5

11. PRACTICE PROBLEMS x = 6 Solve 1. 6x + 3 – 2x + 6 = 33
y = 1
Solve
1. 6x + 3 – 2x + 6 = 33
2. 8(y + 2) + 5 = 29
3. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate?
40h + 2(12h) = 544
$8.50