1. 3-3 day 1 Solve Multi Step Equations
Objective: Students will create and solve equations in one variable.
Standards: A.REI.3 , A.CED.1 , A.REI.1

2. When solving equations always ask yourself 2 questions first:
REMEMBER:
When solving equations always ask yourself 2 questions first:
Can I DISTRIBUTE ?
Can I COMBINE LIKE TERMS ?

3. Example 1 Solve & Justify: 9x + x – 7 = 13 9x + x -7 = 13 10x – 7 = 13
Given
Combine Like
Terms.
10x – 7 = 13
Combine like terms
Get x by itself by doing the opposite operation.
APOE
10x = 20
Simplify
MPOE
x = 2
Simplify

4. y = -4 Example 2 4y – 7 (y – 2) = 26 Given 4y – 7y + 14 = 26
To justify steps must use PROPERTIES
Solve. Justify your steps:
4y – 7 (y – 2) = 26
Use 2-column proof to do this
4y – 7 (y – 2) = 26
Given
4y – 7y + 14 = 26
Distributive Property
-3y + 14 = 26
Combine Like Terms
APOE
-3y = 12
Simplify
MPOE
y = -4
Simplify

5. Homework
Section 3-3 day 1
HW: Pg
SOLVE & PROVE: 3 – 13

6. 3-3 day 2 Solve Multi Step Equations
Objective: Students will create and solve equations in one variable.
Standards: A.REI.3 , A.CED.1 , A.REI.1

7. Example 1 Solve & Justify:3/5(2x – 4) = 18 x = 17 2x – 4 = 30 +4 +4
Multiply by 5/3, the RECIPROCAL of 3/5.
Given
5/3 ∙ 3/5(2x – 4) = 18 ∙ 5/3
MPOE
2x – 4 = 30
Simplify
APOE
2x = 34
Simplify
MPOE
x = 17
Simplify

8. Example 2 25 25 x = 4 hours 20x + 5x + 15 = 115 25x+15=115 -15 -15
You have a pipe broken in your house. The plumber charges a fee of $20 for each hour he is there and also charges an emergency fee of $5 for each hour on top of a one-time $15 charge to look at the problem. You spent $115 to get your plumbing fixed, how many hours was the plumber working?
20x
+ 5x
+ 15
= 115
Remember: “ Per” means this is where the x goes
25x+15=115
STEP 1: Write the equation.
STEP 2: Combine like terms.
Get x by itself by doing the opposite operation.
25x =100
x = 4 hours

9. Homework Section 3-3 day 2 HW: Pg. 150-151 SOLVE & PROVE: 14 – 24
Follow Directions: 38, 39, 40

10. 3-4 Solve Equations with Variables on Both Sides
Objective: Students will create and solve equations in one variable.
Standards: A.REI.3 , A.CED.1 , A.REI.1

11. When solving equations always ask yourself 2 questions first:
REMEMBER:
When solving equations always ask yourself 2 questions first:
Can I DISTRIBUTE ?
Can I COMBINE LIKE TERMS ?

12. x = -2 Example 1 Given -5x -5x -2x = 4 -2 -2
GOAL: Get ALL variables on ONE SIDE, and all NUMBERS on the OTHER SIDE!!
Example 1
Solve. Justify your steps:
-3x + 6x = 5(x + 1) – 1
-3x + 6x = 5(x + 1) – 1
Given
-3x + 6x = 5x + 5 – 1
Distributive Property
3x = 5x + 4
Combine like terms
-5x -5x
APOE
-2x = 4
Simplify
MPOE
x = -2
Simplify

13. Example 2 5x – 6 = 5x - 5 +6 +6 5x – 6 = 5(x – 1) 5x = 5x + 1 -5x -5x
Identify the number of solutions of the equation:
5x – 6 = 5(x – 1)
5x – 6 = 5x - 5
Distribute
APOE.
5x = 5x + 1
-5x -5x
APOE
0 = 1
0 = 1 is NOT TRUE, so the equation has NO SOLUTIONS.

14. Example 3 12x + 8 = 12x + 8 4(3x + 2) = 2(6x + 4)
Identify the number of solutions of the equation:
4(3x + 2) = 2(6x + 4)
12x = 12x + 8
Distribute
The equation is an identity and TRUE , so the solution is ALL REAL NUMBERS.

15. Homework Section 3-4 HW: Pg. 157-158 SOLVE & PROVE: 10 – 13, 22 - 25
FOLLOW DIRECTIONS: 29, 49, 50