170 Chapter 2 Linear Equations and Inequalities a 6 b, a c 6 b c a c 6 b c To illustrate the addition and subtraction properties of inequality, consider the inequality If we add or subtract a real number such as 4 to both sides, the left-hand side will still be greater than the right-hand side. (See Figure 2-11.) 5 > 3 5 4 > 3 4 Figure 2-11 5 7 3. Solving a Linear Inequality Solve the inequality and graph the solution set. Express the solution set in setbuilder notation and in interval notation. Solution: Addition property of inequality (add 3p to both sides). Simplify. Subtraction property of inequality. 2p 5 6 3p 6 2p 3p 5 6 3p 3p 6 Graph: p 5 6 6 p 5 5 6 6 5 p 6 1 5 p 0 p 6 16 Set-builder notation: Interval notation: 1, 12 Skill Practice Solve the inequality and graph the solution set. Express the solution set in set-builder notation and interval notation. 8. 2y 5 6 y 11 2p 5 6 3p 6 Example 4 Answer 8. 5y 0 y 6 66; (, 6) Addition and Subtraction Properties of Inequality Let a, b, and c represent real numbers. 1. *Addition Property of Inequality: If then 2. *Subtraction Property of Inequality: If then *These properties may also be stated for a b, a 7 b, and a b. a 6 b, ( 6 5 4 3 2 1 0 1 2 3 4 5 6 ( 6
miller_beginning_intermediate_algebra_4e_ch1_3
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