Chapter 2 2 Equations Inequalities and Problem Solving

Chapter 2 2 Equations, Inequalities and Problem Solving Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 1

Section 2. 1 Simplifying Algebraic Expressions Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 2

Objective 1 Identifying Terms, Like Terms, and Unlike Terms Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 3

Terms A term is a number or the product of a number and variables raised to powers. The numerical coefficient of a term is the numerical factor. The numerical coefficient of 3 x is 3. Terms Coefficient 7 7 5 x 3 5 ‒ 4 xy 2 ‒ 4 z 2 1 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 4

Example Identify the numerical coefficient of each term. a. ‒ 6 x The numerical coefficient is ‒ 6. b. 27 z 3 c. ‒ y d. The numerical coefficient is 27. The numerical coefficient is ‒ 1. The numerical coefficient is Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 5

Like Terms Like terms contain the same variables raised to the same powers. Terms that are not like terms are called unlike terms. Like Terms Unlike Terms 3 x, 2 x 5 x, 5 x 2 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 6

Example Determine whether the terms are like or unlike. a. b. Unlike c. Like d. Like Unlike Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 7

Objective 2 Combining Like Terms Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 8

Like Terms Simplifying the sum or difference of like terms is called combining like terms. Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 9

Example Simplify each expression by combining like terms. a. 6 x 2 + 7 x 2 = 13 x 2 b. 19 xy – 30 xy = ‒ 11 xy c. 13 xy 2 – 7 x 2 y Can’t be combined (since the terms are not like terms) Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 10

Combining Like Terms To combine like terms, combine the numerical coefficients and multiply the result by the common variable factors. Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 11

Example Simplify each expression by combining like terms. a. 7 y + 2 y + 6 + 10 = (7 + 2)y + (6 + 10) = 9 y + 16 b. 0 – 2 x + 4 + x – 11 = (– 2 + 1)x + (4 – 11) = –x – 7 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 12

Objective 3 Using the Distributive Property Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 13

Example Find each product by using the distributive property to remove parentheses. a. 4(5 x + 7) = 4(5 x) + 4(7)= 20 x + 28 b. ‒ 3(x + 0. 5 y – 7) = ‒ 3(x) + 3(0. 5 y) – (‒ 3)(7) = ‒ 3 x + 1. 5 y + 21 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 14

Example Simplify each expression. a. 4(4 x – 6) + 20 = 16 x – 24 + 20 = 16 x – 4 b. 5 – (3 x + 9) + 6 x = 5 – 3 x – 9 + 6 x = 3 x – 4 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 15

Example Simplify each expression. c. – 3(7 x + 1) – (4 x – 2) = – 21 x – 3 – 4 x + 2 = – 25 x – 1 d. 8 + 11(2 y – 9) = 8 + 22 y – 99 = 22 y – 91 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 16

Objective 4 Writing Word Phrases as Algebraic Expressions Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 17

Example Write each phrase as an algebraic expression and simplify if possible. Let x represent the unknown number. a. Twice a number, plus 9. 2 x + 9 b. Seven times the sum of a number and two. 7 · (x + 2) = 7 · x + 7 · 2 = 7 x + 14 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 18

Example Write each phrase as an algebraic expression and simplify if possible. Let x represent the unknown number. c. Three times the sum of a number and 6 3(x + 6) = 3 x + 18 d. The sum of a number and 2, divided by 5 Copyright © 2017, 2013, 2009 Pearson Education, Inc. Slide 19