172 Chapter 2 Linear Equations and Inequalities Solving a Linear Inequality Solve the inequality and graph the solution set. Express the solution set in set-builder notation and in interval notation. Solution: Add 3 to both sides. 5x 3 12 5x 3 3 12 3 5x 15 5x 5 15 5 x 3 5x ƒ x 36 Set-builder notation: Interval notation: 33, 2 5x 3 12 Example 5 Divide by 5 . Reverse the direction of the inequality sign. 5x 3 12 6 5 4 3 2 1 0 1 2 3 4 5 6 Do not reverse the inequality sign because we are dividing by a positive number. Answer 9. 4 5p ƒ p 6 46; (, 4) TIP: The inequality , could have been solved by isolating x on the right-hand side of the inequality. This would create a positive coefficient on the variable term and eliminate the need to divide by a negative number. Notice that the coefficient of x is positive. 5x 3 12 3 5x 12 15 5x 15 5 5x 5 3 x, or equivalently, x 3 Skill Practice Solve the inequality and graph the solution set. Express the solution set in set-builder notation and in interval notation. 9. Solving a Linear Inequality 5p 2 7 22 Solve the inequality and graph the solution set. Express the solution set in set-builder notation and in interval notation. Solution: Clear parentheses. Combine like terms. Add 4y to both sides. Simplify. Add 6 to both sides. Simplify. 12 21y 32 6 312y 12 2y 12 2y 6 6 6y 3 2y 2y 6 6 4y 3 2y 4y 6 6 4y 4y 3 2y 6 6 3 2y 6 6 6 3 6 2y 6 3 y 6 3 2 2y 2 6 3 2 12 21y 32 6 312y 12 2y Example 6 Divide by 2.The direction of the inequality sign is not reversed because we divided by a positive number.
miller_beginning_intermediate_algebra_4e_ch1_3
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