186 Chapter 2 Linear Equations and Inequalities Using Set-Builder Notation and Interval Notation Example 3 Complete the chart. Set-Builder Interval Notation Graph Notation 5y 0 2 y 6 46 Solution: Set-Builder Interval Notation Graph Notation 1, 32 ( 5x 0 x 6 36 6 5 4 3 2 1 0 1 2 3 4 5 6 32, 42 ( 5y 0 2 y 6 46 6 5 4 3 2 1 0 1 2 3 4 5 6 312 , 2 6 5 4 3 2 1 0 1 2 3 4 5 6 12 5x 0 x 12 6 312 , 2 ( 6 5 4 3 2 1 0 1 2 3 4 5 6 Skill Practice Express each of the following in set-builder notation and interval notation. 7. 3 2 8. 9. ) 2 3 1 x 6 Classroom Examples: pp. 193–194, Exercises 20, 24, and 30 Answers 7. 5x 0 x 26 ; 32, 2 8. ex 0 3 x 6 f a3 ; , b 2 129. 5x 0 3 6 x 16; 3, 14 3. Addition and Subtraction Properties of Inequality The process to solve a linear inequality is very similar to the method used to solve linear equations. Recall that adding or subtracting the same quantity to both sides of an equation results in an equivalent equation.The addition and subtraction properties of inequality state that the same is true for an inequality. Addition and Subtraction Properties of Inequality Let a, b, and c represent real numbers. 1. *Addition Property of Inequality: If 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. 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,
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