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Simplifying -0.5(x + 3) = 2 + -3(0.2 + -0.1x) Reorder the terms: -0.5(3 + x) = 2 + -3(0.2 + -0.1x) (3 * -0.5 + x * -0.5) = 2 + -3(0.2 + -0.1x) (-1.5 + -0.5x) = 2 + -3(0.2 + -0.1x) -1.5 + -0.5x = 2 + (0.2 * -3 + -0.1x * -3) -1.5 + -0.5x = 2 + (-0.6 + 0.3x) Combine like terms: 2 + -0.6 = 1.4 -1.5 + -0.5x = 1.4 + 0.3x Solving -1.5 + -0.5x = 1.4 + 0.3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3x' to each side of the equation. -1.5 + -0.5x + -0.3x = 1.4 + 0.3x + -0.3x Combine like terms: -0.5x + -0.3x = -0.8x -1.5 + -0.8x = 1.4 + 0.3x + -0.3x Combine like terms: 0.3x + -0.3x = 0.0 -1.5 + -0.8x = 1.4 + 0.0 -1.5 + -0.8x = 1.4 Add '1.5' to each side of the equation. -1.5 + 1.5 + -0.8x = 1.4 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.8x = 1.4 + 1.5 -0.8x = 1.4 + 1.5 Combine like terms: 1.4 + 1.5 = 2.9 -0.8x = 2.9 Divide each side by '-0.8'. x = -3.625 Simplifying x = -3.625
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