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Simplifying 0.5(x + -2) + -2(x + -5) = 0.5(x + -5) + -5(x + -2) Reorder the terms: 0.5(-2 + x) + -2(x + -5) = 0.5(x + -5) + -5(x + -2) (-2 * 0.5 + x * 0.5) + -2(x + -5) = 0.5(x + -5) + -5(x + -2) (-1 + 0.5x) + -2(x + -5) = 0.5(x + -5) + -5(x + -2) Reorder the terms: -1 + 0.5x + -2(-5 + x) = 0.5(x + -5) + -5(x + -2) -1 + 0.5x + (-5 * -2 + x * -2) = 0.5(x + -5) + -5(x + -2) -1 + 0.5x + (10 + -2x) = 0.5(x + -5) + -5(x + -2) Reorder the terms: -1 + 10 + 0.5x + -2x = 0.5(x + -5) + -5(x + -2) Combine like terms: -1 + 10 = 9 9 + 0.5x + -2x = 0.5(x + -5) + -5(x + -2) Combine like terms: 0.5x + -2x = -1.5x 9 + -1.5x = 0.5(x + -5) + -5(x + -2) Reorder the terms: 9 + -1.5x = 0.5(-5 + x) + -5(x + -2) 9 + -1.5x = (-5 * 0.5 + x * 0.5) + -5(x + -2) 9 + -1.5x = (-2.5 + 0.5x) + -5(x + -2) Reorder the terms: 9 + -1.5x = -2.5 + 0.5x + -5(-2 + x) 9 + -1.5x = -2.5 + 0.5x + (-2 * -5 + x * -5) 9 + -1.5x = -2.5 + 0.5x + (10 + -5x) Reorder the terms: 9 + -1.5x = -2.5 + 10 + 0.5x + -5x Combine like terms: -2.5 + 10 = 7.5 9 + -1.5x = 7.5 + 0.5x + -5x Combine like terms: 0.5x + -5x = -4.5x 9 + -1.5x = 7.5 + -4.5x Solving 9 + -1.5x = 7.5 + -4.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5x' to each side of the equation. 9 + -1.5x + 4.5x = 7.5 + -4.5x + 4.5x Combine like terms: -1.5x + 4.5x = 3x 9 + 3x = 7.5 + -4.5x + 4.5x Combine like terms: -4.5x + 4.5x = 0.0 9 + 3x = 7.5 + 0.0 9 + 3x = 7.5 Add '-9' to each side of the equation. 9 + -9 + 3x = 7.5 + -9 Combine like terms: 9 + -9 = 0 0 + 3x = 7.5 + -9 3x = 7.5 + -9 Combine like terms: 7.5 + -9 = -1.5 3x = -1.5 Divide each side by '3'. x = -0.5 Simplifying x = -0.5
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