4b. -2(3x + 4) = 6 - 4(x - 2) -6x - 8 = 6 - 4x + 8 Apply the distributive property. -6x - 8=-4x + 14 Combine like terms. -6x - 8 + 4x=-4x + 14 + 4x Add 4x to each side. -2x - 8 = 14 Simplify. -2x - 8 + 8 = 14 + 8 Add 8 to each side. -2x = 22 Simplify. -2x 22 = -2 -2 Divide each side by -2. x=-11 Simplify. The value -11 makes the equation true, so the solution set is 5-116. The check is left for the reader. 4c. 2m 3 + 3 2 = 2m 6¢ 2m 3 + 3 2 ≤ = 6(2m) Multiply each side by the LCD, 6. 6¢ 2m 3 ≤ + 6¢ 3 2 Apply the distributive property on the left and simplify the right side. ≤ = 12m 4m + 9 = 12m Simplify the left side. 4m + 9 - 4m = 12m - 4m Subtract 4m from each side. 9 = 8m Simplify. 9 8m = 8 8 Divide each side by 8. 9 8 = m Simplify. Check: 2m 3 + 3 2 = 2m Begin with the original equation. 2¢ 9 ≤ 8 3 + 3 2 = 2¢ 9 8 ≤ Replace m with 9 8 . 9 4 3 + 3 2 = 9 4 Simplify each product. 9 4 · 1 3 + 3 2 = 9 4 Multiply 9 4 by the reciprocal of 3, 1 3 . 3 4 + 6 4 = 9 4 Simplify the product and write 3 2 as 6 4 . 9 4 = 9 4 Simplify. The value 9 8 makes the equation true, so the solution set is e 9 8 f . 58 Chapter 2 Linear Equations and Inequalities in One Variable
hendricks_intermediate_algebra_1e_ch1_3
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