Section 2.4 More on Solving Linear Equations 125 Solutions 1a. 3x 4 - 5 = x 4 4a3x 4 - 5b = 4a x 4 b Multiply each side by the LCD, 4. 4a3x 4 b - 4(5) = x Apply the distributive property. Simplify. 3x - 20 = x Simplify. 3x - 20 - x = x - x Subtract x from each side. 2x - 20 = 0 Simplify. 2x - 20 + 20 = 0 + 20 Add 20 to each side. 2x = 20 Simplify. 2x 20 = 2 2 Divide each side by 2. x = 10 Simplify. 3x 4 Check: - 5 = x 4 Original equation 3(10) 4 - 5 = 10 4 Replace x with 10. 30 4 - 5 = 10 4 Simplify. 30 4 - 20 4 = 10 4 Subtract the numbers on the left by converting 5 to 20 4 . 10 4 = 10 4 Simplify. Since x = 10 makes the equation a true statement, the solution set is {10}. a 6 1b. - 1 8 = a 12 24aa 6 - 1 8 b = 24a a 12 b Multiply each side by the LCD, 24. 24aa 6 b - 24a1 8 b = 2a Apply the distributive property. Simplify. 4a - 3 = 2a Simplify. 4a - 3 - 2a = 2a - 2a Subtract 2a from each side. 2a - 3 =0 Simplify. 2a - 3 + 3 = 0 + 3 Add 3 to each side. 2a =3 Simplify. 2a 2 = 3 2 Divide each side by 2. a = 3 2 Simplify.
hendricks_beginning_algebra_1e_ch1_3
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