Section 2.2 The Addition Property of Equality 105 �� ������������������������ ������������������ Solve each equation. 3a. 4 + x - 3 = -2 3b. 1.5y - 3 - 4 - 0.5y = 0 3c. 6a - 3 = 5a + 1 3d. 3(x + 2) - (2x - 5) = 0 3e. 3(x + 6) = 4(x - 1) Solutions�� 3a. 4 + x - 3=-2 x + 1=-2 Combine like terms on the left. x + 1 - 1=-2 - 1 Subtract 1 from each side of the equation. x=-3 Simplify. Check: 4 + x - 3=-2 Original equation 4 + (-3) - 3=-2 Replace x with -3. -2=-2 Simplify. Since x = -3 makes the equation true, the solution set is {-3}. 3b. 1.5y - 3 - 4 - 0.5y =0 Combine like terms on the left side. Note that y - 7 =0 1.5y - 0.5y = 1y = y. y - 7 + 7 = 0 + 7 Add 7 to each side. y =7 Simplify. Check: 1.5y - 3 - 4 - 0.5y = 0 Original equation 1.5(7) - 3 - 4 - 0.5(7) = 0 Replace y with 7. 10.5 - 3 - 4 - 3.5 = 0 Simplify each product. 0 = 0 Simplify. Since y = 7 makes the equation true, the solution set is {7}. 3c. 6a - 3 = 5a +1 6a - 3 - 5a = 5a + 1 - 5a Subtract 5a from each side. a - 3 =1 Simplify each side. a - 3 + 3 = 1 + 3 Add 3 to each side. a =4 Simplify. Check: 6a - 3 = 5a + 1 Original equation 6(4) - 3 = 5(4) + 1 Replace a with 4. 24 - 3 = 20 + 1 Find each product. 21 = 21 Simplify each side. Since a = 4 makes the equation true, the solution set is {4}. 3d. 3(x + 2) - 1(2x - 5) = 0 Recall -(2x - 5) = -1(2x - 5). 3x + 6 - 2x + 5 = 0 Apply the distributive property. x + 11 =0 Combine like terms. x + 11 - 11 = 0 - 11 Subtract 11 from each side. x=-11 Simplify.
hendricks_beginning_algebra_1e_ch1_3
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