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Simplifying 0.5(x + 2) + -1(3x + 8) = 1.6(x + -2) + 9 Reorder the terms: 0.5(2 + x) + -1(3x + 8) = 1.6(x + -2) + 9 (2 * 0.5 + x * 0.5) + -1(3x + 8) = 1.6(x + -2) + 9 (1 + 0.5x) + -1(3x + 8) = 1.6(x + -2) + 9 Reorder the terms: 1 + 0.5x + -1(8 + 3x) = 1.6(x + -2) + 9 1 + 0.5x + (8 * -1 + 3x * -1) = 1.6(x + -2) + 9 1 + 0.5x + (-8 + -3x) = 1.6(x + -2) + 9 Reorder the terms: 1 + -8 + 0.5x + -3x = 1.6(x + -2) + 9 Combine like terms: 1 + -8 = -7 -7 + 0.5x + -3x = 1.6(x + -2) + 9 Combine like terms: 0.5x + -3x = -2.5x -7 + -2.5x = 1.6(x + -2) + 9 Reorder the terms: -7 + -2.5x = 1.6(-2 + x) + 9 -7 + -2.5x = (-2 * 1.6 + x * 1.6) + 9 -7 + -2.5x = (-3.2 + 1.6x) + 9 Reorder the terms: -7 + -2.5x = -3.2 + 9 + 1.6x Combine like terms: -3.2 + 9 = 5.8 -7 + -2.5x = 5.8 + 1.6x Solving -7 + -2.5x = 5.8 + 1.6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6x' to each side of the equation. -7 + -2.5x + -1.6x = 5.8 + 1.6x + -1.6x Combine like terms: -2.5x + -1.6x = -4.1x -7 + -4.1x = 5.8 + 1.6x + -1.6x Combine like terms: 1.6x + -1.6x = 0.0 -7 + -4.1x = 5.8 + 0.0 -7 + -4.1x = 5.8 Add '7' to each side of the equation. -7 + 7 + -4.1x = 5.8 + 7 Combine like terms: -7 + 7 = 0 0 + -4.1x = 5.8 + 7 -4.1x = 5.8 + 7 Combine like terms: 5.8 + 7 = 12.8 -4.1x = 12.8 Divide each side by '-4.1'. x = -3.12195122 Simplifying x = -3.12195122
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