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Simplifying 2(x + -1) + 3(x + -1) + 5(x + -1) = 7(1 + -2x) + -2(1 + -2x) Reorder the terms: 2(-1 + x) + 3(x + -1) + 5(x + -1) = 7(1 + -2x) + -2(1 + -2x) (-1 * 2 + x * 2) + 3(x + -1) + 5(x + -1) = 7(1 + -2x) + -2(1 + -2x) (-2 + 2x) + 3(x + -1) + 5(x + -1) = 7(1 + -2x) + -2(1 + -2x) Reorder the terms: -2 + 2x + 3(-1 + x) + 5(x + -1) = 7(1 + -2x) + -2(1 + -2x) -2 + 2x + (-1 * 3 + x * 3) + 5(x + -1) = 7(1 + -2x) + -2(1 + -2x) -2 + 2x + (-3 + 3x) + 5(x + -1) = 7(1 + -2x) + -2(1 + -2x) Reorder the terms: -2 + 2x + -3 + 3x + 5(-1 + x) = 7(1 + -2x) + -2(1 + -2x) -2 + 2x + -3 + 3x + (-1 * 5 + x * 5) = 7(1 + -2x) + -2(1 + -2x) -2 + 2x + -3 + 3x + (-5 + 5x) = 7(1 + -2x) + -2(1 + -2x) Reorder the terms: -2 + -3 + -5 + 2x + 3x + 5x = 7(1 + -2x) + -2(1 + -2x) Combine like terms: -2 + -3 = -5 -5 + -5 + 2x + 3x + 5x = 7(1 + -2x) + -2(1 + -2x) Combine like terms: -5 + -5 = -10 -10 + 2x + 3x + 5x = 7(1 + -2x) + -2(1 + -2x) Combine like terms: 2x + 3x = 5x -10 + 5x + 5x = 7(1 + -2x) + -2(1 + -2x) Combine like terms: 5x + 5x = 10x -10 + 10x = 7(1 + -2x) + -2(1 + -2x) -10 + 10x = (1 * 7 + -2x * 7) + -2(1 + -2x) -10 + 10x = (7 + -14x) + -2(1 + -2x) -10 + 10x = 7 + -14x + (1 * -2 + -2x * -2) -10 + 10x = 7 + -14x + (-2 + 4x) Reorder the terms: -10 + 10x = 7 + -2 + -14x + 4x Combine like terms: 7 + -2 = 5 -10 + 10x = 5 + -14x + 4x Combine like terms: -14x + 4x = -10x -10 + 10x = 5 + -10x Solving -10 + 10x = 5 + -10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10x' to each side of the equation. -10 + 10x + 10x = 5 + -10x + 10x Combine like terms: 10x + 10x = 20x -10 + 20x = 5 + -10x + 10x Combine like terms: -10x + 10x = 0 -10 + 20x = 5 + 0 -10 + 20x = 5 Add '10' to each side of the equation. -10 + 10 + 20x = 5 + 10 Combine like terms: -10 + 10 = 0 0 + 20x = 5 + 10 20x = 5 + 10 Combine like terms: 5 + 10 = 15 20x = 15 Divide each side by '20'. x = 0.75 Simplifying x = 0.75
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