92 Chapter 2 Linear Equations and Inequalities in One Variable We graph the solution set and write the solution set in interval notation and set-builder notation. 46 5 4 5 6 7 8 9 10 11 12 13 14 Interval notation: a46 5 , ∞b Set-builder notation: e x` x > 46 5 f 2f. 4x - 5(x - 2) < 6(x + 1) - 7x 4x - 5x + 10 < 6x + 6 - 7x Apply the distributive property. -x + 10<-x + 6 Combine like terms. -x + 10 + x<-x + 6 + x Add x to each side. 10 < 6 Simplify. The resulting inequality, 10 < 6, is an inequality that is always false. Therefore, the oroginal inequality has no solution. The solution set is the empty set, or . The graph of the solution set is an unshaded number line as shown. –5 –4 –3 –2 –1 0 1 2 3 4 5 2g. x + 5(x - 2) < 3(2x + 1) + 7 x + 5x - 10 < 6x + 3 + 7 Apply the distributive property. 6x - 10 < 6x + 10 Combine like terms. 6x - 10 - 6x < 6x + 10 - 6x Subtract 6x from each side. -10 < 10 Simplify. The resulting inequality, -10 < 10, is always true. Therefore, any real number is a solution of the original inequality. So, the solution set is all real numbers, or . –5 –4 –3 –2 –1 0 1 2 3 4 5 Interval notation: (-∞, ∞) Set-builder notation: 5xux is a real number6 Student Check 2 Solve each inequality. Graph the solution set and write the solution set in interval notation and set-builder notation. a. y + 3<-2 b. -x ≤ 2 c. 7y - 1 > 6 d. 3(a + 2) - 7≥-4a + 10 e. 1 3 y - 2ay + 1 6 b > 2 3 y + 5 6 f. 4(x - 3) + 1 ≥ 5(x + 2) - x g. 7x - 2(4x + 3) < 3(x + 5) - 4x Applications There are a few key phrases that we need to learn before more applications are introduced. Objective 3 ▶ Solve applications of linear inequalities.
hendricks_intermediate_algebra_1e_ch1_3
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