Simplifying Algebraic Expressions envision LESSON 2 3 Simplify

Simplifying Algebraic Expressions envision LESSON 2 -3 Simplify 8 p + 13 p = (8 + 13)p = 21 p Distributive Property Add. 2 -3

Simplifying Algebraic Expressions envision LESSON 2 -3 Simplify q – 9 q = 1 q – 9 q Rewrite q as 1 q. = (1 – 9)q Distributive Property = – 8 q Subtract. 2 -3

Simplifying Algebraic Expressions envision LESSON 2 -3 Simplify 2 h + 4 r + 7 t + h + 3 r + t = 2 h + 1 h + 4 r + 3 r + 7 t + t Commutative Property of Addition = (2 + 1)h + (4 + 3)r + (7 + 1)t Distributive Property = 3 h + 7 r + 8 t Simplify. 2 -3

Simplifying Algebraic Expressions envision LESSON 2 -3 Simplify 4(b – 3) + 2 b = 4 b – 12 + 2 b Distributive Property = 4 b + 2 b – 12 Commutative Property of Addition = (4 + 2)b – 12 Distributive Property = 6 b – 12 Simplify. 2 -3

Simplifying Algebraic Expressions envision LESSON 2 -3 Simplify 7 t – 2(t – 3) = 7 t + (– 2)(t – 3) Add the opposite of 2(t – 3). = 7 t + [– 2 t – (– 6)] Distributive Property = 7 t + (– 2 t) + 6 Simplify. = [7 + (– 2)]t + 6 Distributive Property = 5 t + 6 Simplify. 2 -3

Simplifying Algebraic Expressions envision LESSON 2 -3 Simplify each expression. 1. 3 h + 7 h 10 h 2. – 13 c + c – 12 c 3. 4 y – 7 + 8 y 12 y – 7 4. 1 – 6(b – 9) – 6 b + 55 2 -3

Solving Multi-Step Equations envision LESSON 2 -1 (For help, go to Lesson 2 -3. ) Simplify each expression. 1. 12 d – 6 + 4 d 2. 5 – 3 m + 17 – 23 m 3. 4(7 – 3 r) 4. 9(t + 7) – 16 5. (q + 1)5 + 3 q 6. 12 – 6(2 r – 8) 7. Explain how to simplify 2 x – (5 x + 7). 2 -1

Solving Multi-Step Equations envision LESSON 2 -1 Solutions 1. 12 d + 4 d – 6 = (12 + 4)d – 6 = 16 d – 6 2. (5 + 17) + (– 3 – 23)m = 22 – 26 m 3. 4(7) + (4)(– 3 r) = 28 – 12 r 4. 9(t) + 9(7) – 16 = 9 t + 63 – 16 = 9 t + 47 5. 5(q) + 5(1) + 3 q = (5 + 3)q + 5 = 8 q + 5 6. 12 + (– 6)(2 r) + (– 6)(– 8) = 12 – 12 r + 48 = 60 – 12 r 7. First, distribute the negative to get 2 x – 5 x – 7. Then combine like terms to get – 3 x – 7. 2 -1

Solving Multi-Step Equations envision LESSON 2 -1 Solve 2 c + 2 + 3 c = 12 2 c + 3 c + 2 = 12 5 c + 2 – 2 = 12 – 2 5 c = 10 5 c 10 = 5 5 c=2 Commutative Property Combine like terms. Subtract 2 from each side. Simplify. Divide each side by 5. Simplify. 2 -1

Solving Multi-Step Equations envision LESSON 2 -1 (continued) Check 2 c + 2 + 3 c = 12 2(2) + 2 + 3(2) 12 12 = 12 Substitute 2 for c. The solution checks. 2 -1

Solving Multi-Step Equations envision LESSON 2 -1 Eight cheerleaders set a goal of selling 424 boxes of cards to raise money. After two weeks, each cheerleader has sold 28 boxes. Write and solve an equation to find out how many more boxes each cheerleader must sell. Words 8 cheerleaders • (28 boxes + additional boxes = 424 boxes Let x = the number of additional boxes. Equation 8 • (28 8(28 + x) = 424 2 -1 + x) = 424

Solving Multi-Step Equations envision LESSON 2 -1 (continued) 224 + 8 x = 424 224 – 224 + 8 x = 424 – 224 Distributive Property Subtract 224 from each side. 8 x = 200 Simplify. 8 x 200 = 8 8 Divide each side by 8. x = 25 Simplify. Each cheerleader must sell 25 more boxes. Check for Reasonableness Round 8 to 10 and 28 to 20. The cheerleaders sold about 10 • 20, or 200 boxes. This means each cheerleader must sell about 22 more boxes. 25 is close to 22. The answer is reasonable. 2 -1

Solving Multi-Step Equations envision LESSON 2 -1 1. Solve 4(3 u – 1) = 20. 2. Solve 5 t – 4 – t = – 8. – 1 2 2 -1