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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: 9x + x – 7 = 13 Combine Like 9x + x -7 = 13 Given Terms. 10x – 7 = 13 Combine like terms Get x by itself +7 +7 APOE by doing the 10x = 20 Simplify opposite operation. 10 10 MPOE x = 2 Simplify To justify steps must use Solve. Justify your steps: PROPERTIES Use 2-column 4y – 7 (y – 2) = 26 proof to do this Example 2 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 3/5(2x – 4) = 18 5/3 ∙ 3/5(2x – 4) = 18 2x – 4 = 30 +4 +4 2x = 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. 20x + 5x + 15 = 115 25x+15=115 -15 -15 25x =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 -3x + 6x = 5(x + 1) – 1 proof to do this -3x + 6x = 5(x + 1) – 1 Given Example 1 -3x + 6x = 5x + 5 – 1 Distributive Property Simplify 3x = 5x + 4 -5x -5x -2x = 4 -2 -2 x = -2 APOE Simplify MPOE Simplify Example 2 Identify the number of solutions of the equation: 5x – 6 = 5(x – 1) 5x – 6 = 5x - 5 +6 +6 5x = 5x + 1 -5x -5x 0= 1 Distribute Add 6 to both sides. Subtract 5x 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(3x + 2) = 2(6x + 4) 12x + 8 = 12x + 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