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Simplifying 0.5x + 2(1.3x + -1.2) = 5(1.2x + 0.6) + -0.2x Reorder the terms: 0.5x + 2(-1.2 + 1.3x) = 5(1.2x + 0.6) + -0.2x 0.5x + (-1.2 * 2 + 1.3x * 2) = 5(1.2x + 0.6) + -0.2x 0.5x + (-2.4 + 2.6x) = 5(1.2x + 0.6) + -0.2x Reorder the terms: -2.4 + 0.5x + 2.6x = 5(1.2x + 0.6) + -0.2x Combine like terms: 0.5x + 2.6x = 3.1x -2.4 + 3.1x = 5(1.2x + 0.6) + -0.2x Reorder the terms: -2.4 + 3.1x = 5(0.6 + 1.2x) + -0.2x -2.4 + 3.1x = (0.6 * 5 + 1.2x * 5) + -0.2x -2.4 + 3.1x = (3 + 6x) + -0.2x Combine like terms: 6x + -0.2x = 5.8x -2.4 + 3.1x = 3 + 5.8x Solving -2.4 + 3.1x = 3 + 5.8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.8x' to each side of the equation. -2.4 + 3.1x + -5.8x = 3 + 5.8x + -5.8x Combine like terms: 3.1x + -5.8x = -2.7x -2.4 + -2.7x = 3 + 5.8x + -5.8x Combine like terms: 5.8x + -5.8x = 0.0 -2.4 + -2.7x = 3 + 0.0 -2.4 + -2.7x = 3 Add '2.4' to each side of the equation. -2.4 + 2.4 + -2.7x = 3 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -2.7x = 3 + 2.4 -2.7x = 3 + 2.4 Combine like terms: 3 + 2.4 = 5.4 -2.7x = 5.4 Divide each side by '-2.7'. x = -2 Simplifying x = -2
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