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Section 3.2 Addition and Subtraction Properties of Equality 141 x 7 x 7 Substitute 7 for x. 7 7 z 3 8 z 3 8 5 3 8 8 8 6p 18 3 6p 18 6132 18 Avoiding Mistakes It is important to distinguish between an equation and an expression. An equation has an equal sign, whereas an expression does not. For example: 2x 4 16 equation 7x 9 expression Determining Whether a Number Is a Solution to an Equation Example 1 Determine whether the given number is a solution to the equation. a. 2x 9 3; 6 b. 20 8p 4; 2 Solution: a. 2x – 9 3 Substitute 6 for x. Simplify. ✓ The right-hand side equals the left-hand side. Thus, 6 is a solution to the equation 2x 9 3. 2162 9 3 12 9 3 3 3 b. 20 8p – 4 Substitute 2 for p. Simplify. The right-hand side does not equal the left-hand side. Thus, 2 is not a solution to the equation 20 8p – 4. 20 8122 4 20 16 4 20 20 Answers 1. Equation 2. Expression 3. Yes 4. No In the study of algebra, you will encounter a variety of equations. In this chapter, we will focus on a specific type of equation called a linear equation in one variable. Concept Connections Identify as an expression or an equation. 1. 2w 6 2. x 8 Skill Practice Determine whether the given number is a solution to the equation. 3. 2 3x 23; 7 4. 9 4x 1; 2 Equation Solution Check 7 ✓ 5 Substitute 5 for z. ✓ Substitute 3 for p. 18 18 ✓ The right-hand side equals the lefthand side. The right-hand side equals the lefthand side. The right-hand side equals the lefthand side.


miller_prealgebra_2e_ch1_3
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