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 Terms x = 20 10x – 7 = x = 2 Get x by itself by doing the opposite operation. Given Combine like terms APOE Simplify 9x + x -7 = 13 MPOE Simplify

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

Homework Section 3-3 day 1 HW: Pg 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 Multiply by 5/3, the RECIPROCAL of 3/5. 2x – 4 = 30 2x = 34 5/3 ∙ 3/5 (2x – 4) = 18 ∙ 5/3 2 2 x = /5 (2x – 4) = 18 Given MPOE APOE 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? STEP 1: Write the equation. 20x + 5x+ 15= 115 STEP 2: Combine like terms. 25x+15=115 Get x by itself by doing the opposite operation x = x = 4 hours Remember: “ Per” means this is where the x goes

Homework Section 3-3 day 2 HW: Pg 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 ?

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

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

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

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