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Simplifying 0.5(x + -0.2) + -1.5(2x + -0.4) = 2.5(3x + 1) Reorder the terms: 0.5(-0.2 + x) + -1.5(2x + -0.4) = 2.5(3x + 1) (-0.2 * 0.5 + x * 0.5) + -1.5(2x + -0.4) = 2.5(3x + 1) (-0.1 + 0.5x) + -1.5(2x + -0.4) = 2.5(3x + 1) Reorder the terms: -0.1 + 0.5x + -1.5(-0.4 + 2x) = 2.5(3x + 1) -0.1 + 0.5x + (-0.4 * -1.5 + 2x * -1.5) = 2.5(3x + 1) -0.1 + 0.5x + (0.6 + -3x) = 2.5(3x + 1) Reorder the terms: -0.1 + 0.6 + 0.5x + -3x = 2.5(3x + 1) Combine like terms: -0.1 + 0.6 = 0.5 0.5 + 0.5x + -3x = 2.5(3x + 1) Combine like terms: 0.5x + -3x = -2.5x 0.5 + -2.5x = 2.5(3x + 1) Reorder the terms: 0.5 + -2.5x = 2.5(1 + 3x) 0.5 + -2.5x = (1 * 2.5 + 3x * 2.5) 0.5 + -2.5x = (2.5 + 7.5x) Solving 0.5 + -2.5x = 2.5 + 7.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5x' to each side of the equation. 0.5 + -2.5x + -7.5x = 2.5 + 7.5x + -7.5x Combine like terms: -2.5x + -7.5x = -10x 0.5 + -10x = 2.5 + 7.5x + -7.5x Combine like terms: 7.5x + -7.5x = 0.0 0.5 + -10x = 2.5 + 0.0 0.5 + -10x = 2.5 Add '-0.5' to each side of the equation. 0.5 + -0.5 + -10x = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -10x = 2.5 + -0.5 -10x = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 -10x = 2 Divide each side by '-10'. x = -0.2 Simplifying x = -0.2
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