1. 3.3 Using the Properties Together
Goals:
To solve equation by using the addition and multiplication properties
To solve equation by collecting like terms
To solve equations by distributing

2. Steps to Solve Multi-Step Equations
Distribute
Collect like terms on each side of the =
Add/ Subtract (APE)
Multiply / Divide (MPE)

3. 3x + 4 = 13
2-step equations: Always do the add/subtract step before multiplying by the inverse of the coefficient.

4. Solve: 3x + 4 = 13
3x + 4 = 13
3x = 9 3
x = 3

5. Solve: -5x + 6 = 21
-5x + 6 = 21
-5x = 15 -5
x = -3

6. 6x + 2x = 16
If there are like terms on one side of the equation, collect them before using the properties
8x = 16
x = 2

7. 9x - 4x = 20
5x = 20 5

8. 9x + 3x – 5 = 19
12x – 5 = 19 +5
12x = 24
x = 2

9. 2(2y + 3) = 14
When there are parenthesis, you will normally apply the distributive property first.
4y + 6 = 14
4y = 8
y = 2

10. Solve: 8(3x - 2) = 56
+16

11. Collect like terms on the same side of equation.
Distribute
Collect like terms on the same side of equation.
Add the opposite of any number being added to “x”
Divide both sides by the coefficient of “x”.
4(x - 2) + 3(2x + 1) = 5
4x x + 3 = 5
10x – 5 = 5
10x – 5 +5 = 5 + 5
10x = 10 10 10
x = 1

12. Collect like terms on the same side of equation.
Distribute
Collect like terms on the same side of equation.
Add the opposite of any number being added to “x”
Divide both sides by the coefficient of “x”.
3(2x - 1) - 5(x + 4) = 61
6x x - 20 = 61
1x -23 = 61
+23
1x = 84 1
x = 84

13. Assignment: Page 127 #’s (4-40) even