1. Math Journal 9-29
𝑥 −16=− 𝑥 −10=10
𝑥 =− −8𝑥 =− 𝑥 =12

2. Unit 3 Day 2: Solving Multi-Step Equations
Essential Question: How do I solve equations that require more than two steps?

3. Vocabulary
Like Terms: terms whose variables and exponents are the same.
Distributive Property: 𝒂(𝒃 + 𝒄) = 𝒂𝒃 + 𝒂𝒄

4. Solving Multi-Step Equations
Simplify:
1) Apply the distributive property, if necessary.
2) Combine like terms on each side of the equal sign.
Solve:
Solve using the steps from Day 1.
Check:
4) Plug in the solution to see if it satisfies the equation!

5. Example 1: Solve the equations.
a) x – 3 = -9
+ 3
+ 3
x = -6 3 5
b) x = -6
5 ·
· 5
To get rid of a fraction:
1) Multiply by the denominator
2) Divide by the numerator OR
Multiply by the reciprocal
3x = -30 3 3
x = -10

6. Example 2: Solve the equations. a) 7x – 3x – 8 = 24 b) 4x – 8 + x = 2
+ 8
+ 8
+ 8
+ 8 4x
= 32 5x
= 10 4 4 5 5 x
= 8
x = 2

7. Example 3: Solve the equations.
a) x – 9x + 17 = -4 b) 4x – 9 + 3x = 5
-7x
+ 17
= -4 7x
– 9 = 5
- 17
- 17
+ 9
+ 9
-7x
= -21 7x
= 14 -7 -7 7 7
x = 2 x
= 3

8. Example 4: Solve the equations.
a) x + 3(x + 4) = 28 b) 4x – 3(x – 2) = 21 5x
+ 3x
+ 12 = 28 4x
– 3x
+ 6 = 21 8x
+ 12 = 28 x
+ 6 = 21
- 6
- 6
- 12
- 12 8x
= 16
x = 15 8 8 x
= 2

9. Example 5: Solve the equations.
a) x + 12(x – 3) = b) x – 5(x – 9) = 27 4x
+ 12x
– 36 = 28 2x
– 5x
+ 45 = 27
16x
– 36 = 28
-3x
+ 45 = 27
+ 36
+ 36
- 45
- 45
-3x
= -18
16x
= 64 16 16 -3 -3 x
= 4
x = 6

10. Summary
Essential Question: How do I solve equations that require more than two steps?
Take 1 minute to write 2 sentences answering the essential question.