Section 2.4 Linear Inequalities and Applications 91 We graph the solution set and write the solution set in interval notation and set-builder notation. –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 Interval notation: (-∞, -7 Set-builder notation: 5aua≤-76 Check: We will check two values to make sure our answer is reasonable. a=-8 (in solution set): a = 1 (not in solution set): -2a - 4 ≥ 10 -2a - 4 ≥ 10 -2(-8) - 4 ≥ 10 -2(1) - 4 ≥ 10 16 - 4 ≥ 10 -2 - 4 ≥ 10 12 ≥ 10 True -6 ≥ 10 False 2d. 3(2y - 4) - (y + 3) ≥ 5(3y + 1) 6y - 12 - y - 3 ≥ 15y + 5 5y - 15 ≥ 15y + 5 5y - 15 + 15 ≥ 15y + 5 + 15 5y ≥ 15y + 20 5y - 15y ≥ 15y + 20 - 15y -10y ≥ 20 -10y ≤ -10 20 -10 y≤-2 We graph the solution set and write the solution set in interval notation and set-builder notation. –7 –6 –5 –4 –3 –2 –1 0 1 2 3 Interval notation: (-∞, -2 Set-builder notation: 5yuy≤-26 2e. 3 2 (x - 5) > 1 4 x + 4 4 c 3 2 (x - 5)d > 4a1 4 x + 4b 6(x - 5) > x + 16 6x - 30 > x + 16 6x - 30 + 30 > x + 16 + 30 6x > x + 46 6x - x > x + 46 - x 5x > 46 5x > 5 46 5 x > 46 5 Apply the distributive property. Combine like terms. Add 15 to each side. Simplify. Subtract 15y from each side. Simplify. Divide each side by -10 and reverse the inequality symbol. Simplify. Multiply each side by the LCD, 4. Simplify on the left: 4a 3 2 b = 12 2 = 6 and apply the distributive property on the right. Apply the distributive property. Add 30 to each side. Simplify. Subtract x from each side. Simplify. Divide each side by 5. Simplify.
hendricks_intermediate_algebra_1e_ch1_3
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