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Simplifying 0.5(6 + 4x) + -0.5(8x + -12) = 0.5(2x + -4) (6 * 0.5 + 4x * 0.5) + -0.5(8x + -12) = 0.5(2x + -4) (3 + 2x) + -0.5(8x + -12) = 0.5(2x + -4) Reorder the terms: 3 + 2x + -0.5(-12 + 8x) = 0.5(2x + -4) 3 + 2x + (-12 * -0.5 + 8x * -0.5) = 0.5(2x + -4) 3 + 2x + (6 + -4x) = 0.5(2x + -4) Reorder the terms: 3 + 6 + 2x + -4x = 0.5(2x + -4) Combine like terms: 3 + 6 = 9 9 + 2x + -4x = 0.5(2x + -4) Combine like terms: 2x + -4x = -2x 9 + -2x = 0.5(2x + -4) Reorder the terms: 9 + -2x = 0.5(-4 + 2x) 9 + -2x = (-4 * 0.5 + 2x * 0.5) 9 + -2x = (-2 + 1x) Solving 9 + -2x = -2 + 1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 9 + -2x + -1x = -2 + 1x + -1x Combine like terms: -2x + -1x = -3x 9 + -3x = -2 + 1x + -1x Combine like terms: 1x + -1x = 0 9 + -3x = -2 + 0 9 + -3x = -2 Add '-9' to each side of the equation. 9 + -9 + -3x = -2 + -9 Combine like terms: 9 + -9 = 0 0 + -3x = -2 + -9 -3x = -2 + -9 Combine like terms: -2 + -9 = -11 -3x = -11 Divide each side by '-3'. x = 3.666666667 Simplifying x = 3.666666667
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