Section 2.3 The Multiplication Property of Equality 115 �� Solutions�� 2a. We need to isolate the variable term, 2x, on one side of the equation. One way to do this is to subtract 1 from both sides. 2x + 1=-5 2x + 1 - 1=-5 - 1 Subtract 1 from each side. 2x=-6 Simplify. 2x 2 = -6 2 x=-3 Divide each side by 2. Simplify. Check: 2x + 1=-5 Original equation 2(-3) + 1=-5 Replace x with -3. -6 + 1=-5 Simplify. -5=-5 Simplify. Since x = -3 makes the equation is true, the solution set is {-3}. 2b. We need to remove a variable term from either the left side or the right side of the equation. One way to do this is to add 2y to both sides. 4y + 3=-2y -9 4y + 3 + 2y=-2y - 9 + 2y Add 2y to each side. 6y + 3=-9 Simplify. 6y + 3 - 3=-9 - 3 Subtract 3 from each side. 6y=-12 Simplify. 6y 6 = -12 6 Divide each side by 6. y=-2 Simplify. Check: 4y + 3=-2y - 9 Original equation 4(-2) + 3=-2(-2) - 9 Replace y with -2. -8 + 3 = 4 - 9 Simplify. -5=-5 Simplify. Since y = -2 makes the equation true, the solution set is {-2}. ������������ We would have obtained the same solution of this equation if we had subtracted 4y from both sides. 4y + 3=-2y - 9 4y + 3 - 4y=-2y - 9 - 4y Subtract 4y from each side. 3=-6y -9 Simplify. 3 + 9=-6y - 9 + 9 Add 9 to each side. 12=-6y Simplify. 12 -6 = -6y -6 Divide each side by -6. -2 = y Simplify. 2c. 5x - 3 - 2x = 8x -1 3x - 3 = 8x -1 Combine like terms on the left. 3x - 3 - 3x = 8x - 1 - 3x Subtract 3x from each side. -3 = 5x -1 Simplify. -3 + 1 = 5x - 1 + 1 Add 1 to each side. -2 = 5x Simplify. 2 5x -= 5 5 Divide each side by 5. - 2 5 = x Simplify.
hendricks_beginning_algebra_1e_ch1_3
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