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Simplifying 5(x + -9) = 0.5(x + -6) + 0.5(x + 8) Reorder the terms: 5(-9 + x) = 0.5(x + -6) + 0.5(x + 8) (-9 * 5 + x * 5) = 0.5(x + -6) + 0.5(x + 8) (-45 + 5x) = 0.5(x + -6) + 0.5(x + 8) Reorder the terms: -45 + 5x = 0.5(-6 + x) + 0.5(x + 8) -45 + 5x = (-6 * 0.5 + x * 0.5) + 0.5(x + 8) -45 + 5x = (-3 + 0.5x) + 0.5(x + 8) Reorder the terms: -45 + 5x = -3 + 0.5x + 0.5(8 + x) -45 + 5x = -3 + 0.5x + (8 * 0.5 + x * 0.5) -45 + 5x = -3 + 0.5x + (4 + 0.5x) Reorder the terms: -45 + 5x = -3 + 4 + 0.5x + 0.5x Combine like terms: -3 + 4 = 1 -45 + 5x = 1 + 0.5x + 0.5x Combine like terms: 0.5x + 0.5x = 1x -45 + 5x = 1 + 1x Solving -45 + 5x = 1 + 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. -45 + 5x + -1x = 1 + 1x + -1x Combine like terms: 5x + -1x = 4x -45 + 4x = 1 + 1x + -1x Combine like terms: 1x + -1x = 0 -45 + 4x = 1 + 0 -45 + 4x = 1 Add '45' to each side of the equation. -45 + 45 + 4x = 1 + 45 Combine like terms: -45 + 45 = 0 0 + 4x = 1 + 45 4x = 1 + 45 Combine like terms: 1 + 45 = 46 4x = 46 Divide each side by '4'. x = 11.5 Simplifying x = 11.5
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