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

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

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

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

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

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

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

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

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

Solving Multi-Step Equations envision LESSON 2-1 (continued) Check 2c + 2 + 3c = 12 2(2) + 2 + 3(2) 12 Substitute 2 for c. 12 = 12 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. Let x = the number of additional boxes. Words 8 cheerleaders • (28 boxes + = 424 boxes Equation 8 • (28 + x) = 424 additional boxes 8(28 + x) = 424 2-1

Solving Multi-Step Equations envision LESSON 2-1 (continued) 224 + 8x = 424 Distributive Property 224 – 224 + 8x = 424 – 224 Subtract 224 from each side. 8x = 200 Simplify. Divide each side by 8. 8x 8 = 200 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(3u –1) = 20. 2. Solve 5t – 4 – t = – 8. 2 –1 2-1