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

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 ?

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 +7 +7 Get x by itself by doing the opposite operation. APOE 10x = 20 Simplify 10 10 MPOE x = 2 Simplify

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 -14 -14 APOE -3y = 12 Simplify -3 -3 MPOE y = -4 Simplify

Homework Section 3-3 day 1 HW: Pg. 150-151 SOLVE & PROVE: 3 – 13

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

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 +4 +4 APOE 2x = 34 Simplify 2 2 MPOE x = 17 Simplify

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. -15 -15 STEP 2: Combine like terms. Get x by itself by doing the opposite operation. 25x =100 25 25 x = 4 hours

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

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

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 ?

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 -2 -2 MPOE x = -2 Simplify

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 +6 +6 APOE. 5x = 5x + 1 -5x -5x APOE 0 = 1 0 = 1 is NOT TRUE, so the equation has NO SOLUTIONS.

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 + 8 = 12x + 8 Distribute The equation is an identity and TRUE , so the solution is ALL REAL NUMBERS.

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