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Simplifying 0.1(x + 0.5) + 0.2x = 0.2(x + -0.4) Reorder the terms: 0.1(0.5 + x) + 0.2x = 0.2(x + -0.4) (0.5 * 0.1 + x * 0.1) + 0.2x = 0.2(x + -0.4) (0.05 + 0.1x) + 0.2x = 0.2(x + -0.4) Combine like terms: 0.1x + 0.2x = 0.3x 0.05 + 0.3x = 0.2(x + -0.4) Reorder the terms: 0.05 + 0.3x = 0.2(-0.4 + x) 0.05 + 0.3x = (-0.4 * 0.2 + x * 0.2) 0.05 + 0.3x = (-0.08 + 0.2x) Solving 0.05 + 0.3x = -0.08 + 0.2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2x' to each side of the equation. 0.05 + 0.3x + -0.2x = -0.08 + 0.2x + -0.2x Combine like terms: 0.3x + -0.2x = 0.1x 0.05 + 0.1x = -0.08 + 0.2x + -0.2x Combine like terms: 0.2x + -0.2x = 0.0 0.05 + 0.1x = -0.08 + 0.0 0.05 + 0.1x = -0.08 Add '-0.05' to each side of the equation. 0.05 + -0.05 + 0.1x = -0.08 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + 0.1x = -0.08 + -0.05 0.1x = -0.08 + -0.05 Combine like terms: -0.08 + -0.05 = -0.13 0.1x = -0.13 Divide each side by '0.1'. x = -1.3 Simplifying x = -1.3
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