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}. Note: 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_intermediate_algebra_1e_ch1_3
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