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Simplifying 5(2x + -6) + -2(3x + -5) + 4(x + -1) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Reorder the terms: 5(-6 + 2x) + -2(3x + -5) + 4(x + -1) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x (-6 * 5 + 2x * 5) + -2(3x + -5) + 4(x + -1) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x (-30 + 10x) + -2(3x + -5) + 4(x + -1) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Reorder the terms: -30 + 10x + -2(-5 + 3x) + 4(x + -1) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x -30 + 10x + (-5 * -2 + 3x * -2) + 4(x + -1) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x -30 + 10x + (10 + -6x) + 4(x + -1) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Reorder the terms: -30 + 10x + 10 + -6x + 4(-1 + x) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x -30 + 10x + 10 + -6x + (-1 * 4 + x * 4) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x -30 + 10x + 10 + -6x + (-4 + 4x) = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Reorder the terms: -30 + 10 + -4 + 10x + -6x + 4x = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Combine like terms: -30 + 10 = -20 -20 + -4 + 10x + -6x + 4x = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Combine like terms: -20 + -4 = -24 -24 + 10x + -6x + 4x = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Combine like terms: 10x + -6x = 4x -24 + 4x + 4x = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Combine like terms: 4x + 4x = 8x -24 + 8x = 0.5(8x + -6) + -3(x + -2) + 4(2x + -5) + -8x Reorder the terms: -24 + 8x = 0.5(-6 + 8x) + -3(x + -2) + 4(2x + -5) + -8x -24 + 8x = (-6 * 0.5 + 8x * 0.5) + -3(x + -2) + 4(2x + -5) + -8x -24 + 8x = (-3 + 4x) + -3(x + -2) + 4(2x + -5) + -8x Reorder the terms: -24 + 8x = -3 + 4x + -3(-2 + x) + 4(2x + -5) + -8x -24 + 8x = -3 + 4x + (-2 * -3 + x * -3) + 4(2x + -5) + -8x -24 + 8x = -3 + 4x + (6 + -3x) + 4(2x + -5) + -8x Reorder the terms: -24 + 8x = -3 + 4x + 6 + -3x + 4(-5 + 2x) + -8x -24 + 8x = -3 + 4x + 6 + -3x + (-5 * 4 + 2x * 4) + -8x -24 + 8x = -3 + 4x + 6 + -3x + (-20 + 8x) + -8x Reorder the terms: -24 + 8x = -3 + 6 + -20 + 4x + -3x + 8x + -8x Combine like terms: -3 + 6 = 3 -24 + 8x = 3 + -20 + 4x + -3x + 8x + -8x Combine like terms: 3 + -20 = -17 -24 + 8x = -17 + 4x + -3x + 8x + -8x Combine like terms: 4x + -3x = 1x -24 + 8x = -17 + 1x + 8x + -8x Combine like terms: 1x + 8x = 9x -24 + 8x = -17 + 9x + -8x Combine like terms: 9x + -8x = 1x -24 + 8x = -17 + 1x Solving -24 + 8x = -17 + 1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. -24 + 8x + -1x = -17 + 1x + -1x Combine like terms: 8x + -1x = 7x -24 + 7x = -17 + 1x + -1x Combine like terms: 1x + -1x = 0 -24 + 7x = -17 + 0 -24 + 7x = -17 Add '24' to each side of the equation. -24 + 24 + 7x = -17 + 24 Combine like terms: -24 + 24 = 0 0 + 7x = -17 + 24 7x = -17 + 24 Combine like terms: -17 + 24 = 7 7x = 7 Divide each side by '7'. x = 1 Simplifying x = 1
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