3 -3 day 1 Solve Multi Step Equations

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

REMEMBER: When solving equations always ask yourself 2 questions first: 1. Can I DISTRIBUTE ? 2. Can I COMBINE LIKE TERMS ?

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

To justify steps must use Solve. Justify your steps: PROPERTIES Use 2 -column 4 y – 7 (y – 2) = 26 proof to do this Example 2 4 y – 7 (y – 2) = 26 Given 4 y – 7 y + 14 = 26 Distributive Property -3 y + 14 = 26 Combine Like Terms -14 APOE -3 y = 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(2 x – 4) = 18 5/3 ∙ 3/5(2 x – 4) = 18 2 x – 4 = 30 +4 +4 2 x = 34 2 2 x = 17 Multiply by Given 5/3, the ∙ 5/3 MPOE RECIPROCAL Simplify of 3/5. APOE Simplify MPOE Simplify

Example 2 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? Remember: “ Per” means this is where the x goes STEP 1: Write the equation. STEP 2: Combine like terms. 20 x + 5 x + 15 = 115 25 x+15=115 -15 25 x =100 25 25 Get x by itself by doing the opposite operation. 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

REMEMBER: When solving equations always ask yourself 2 questions first: 1. Can I DISTRIBUTE ? 2. Can I COMBINE LIKE TERMS ?

To justify steps must use Solve. Justify your steps: PROPERTIES Use 2 -column -3 x + 6 x = 5(x + 1) – 1 proof to do this -3 x + 6 x = 5(x + 1) – 1 Given Example 1 -3 x + 6 x = 5 x + 5 – 1 3 x = 5 x + 4 -5 x -2 x = 4 -2 -2 x = -2 Distributive Property Simplify APOE Simplify MPOE Simplify

Example 2 Identify the number of solutions of the equation: 5 x – 6 = 5(x – 1) 5 x – 6 = 5 x - 5 +6 +6 5 x = 5 x + 1 -5 x 0= 1 Distribute Add 6 to both sides. Subtract 5 x from both sides. 0 = 1 is NOT TRUE, so the equation has NO SOLUTIONS.

Example 3 Identify the number of solutions of the equation: 4(3 x + 2) = 2(6 x + 4) 12 x + 8 = 12 x + 8 Distribute The equation is an identity and 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