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Simplifying 0.5(6 + 4x) + -0.25(8x + -12) = 0.5(2x + -4) (6 * 0.5 + 4x * 0.5) + -0.25(8x + -12) = 0.5(2x + -4) (3 + 2x) + -0.25(8x + -12) = 0.5(2x + -4) Reorder the terms: 3 + 2x + -0.25(-12 + 8x) = 0.5(2x + -4) 3 + 2x + (-12 * -0.25 + 8x * -0.25) = 0.5(2x + -4) 3 + 2x + (3 + -2x) = 0.5(2x + -4) Reorder the terms: 3 + 3 + 2x + -2x = 0.5(2x + -4) Combine like terms: 3 + 3 = 6 6 + 2x + -2x = 0.5(2x + -4) Combine like terms: 2x + -2x = 0 6 + 0 = 0.5(2x + -4) 6 = 0.5(2x + -4) Reorder the terms: 6 = 0.5(-4 + 2x) 6 = (-4 * 0.5 + 2x * 0.5) 6 = (-2 + 1x) Solving 6 = -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. 6 + -1x = -2 + 1x + -1x Combine like terms: 1x + -1x = 0 6 + -1x = -2 + 0 6 + -1x = -2 Add '-6' to each side of the equation. 6 + -6 + -1x = -2 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = -2 + -6 -1x = -2 + -6 Combine like terms: -2 + -6 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8
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