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Simplifying -31 + -1[2 + 5x + -7(x + 2)] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] Reorder the terms: -31 + -1[2 + 5x + -7(2 + x)] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] -31 + -1[2 + 5x + (2 * -7 + x * -7)] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] -31 + -1[2 + 5x + (-14 + -7x)] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] Reorder the terms: -31 + -1[2 + -14 + 5x + -7x] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] Combine like terms: 2 + -14 = -12 -31 + -1[-12 + 5x + -7x] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] Combine like terms: 5x + -7x = -2x -31 + -1[-12 + -2x] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] -31 + [-12 * -1 + -2x * -1] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] -31 + [12 + 2x] = -9(2x + -5) + -1[5(x + -1) + -3x + 3] Combine like terms: -31 + 12 = -19 -19 + 2x = -9(2x + -5) + -1[5(x + -1) + -3x + 3] Reorder the terms: -19 + 2x = -9(-5 + 2x) + -1[5(x + -1) + -3x + 3] -19 + 2x = (-5 * -9 + 2x * -9) + -1[5(x + -1) + -3x + 3] -19 + 2x = (45 + -18x) + -1[5(x + -1) + -3x + 3] Reorder the terms: -19 + 2x = 45 + -18x + -1[5(-1 + x) + -3x + 3] -19 + 2x = 45 + -18x + -1[(-1 * 5 + x * 5) + -3x + 3] -19 + 2x = 45 + -18x + -1[(-5 + 5x) + -3x + 3] Reorder the terms: -19 + 2x = 45 + -18x + -1[-5 + 3 + 5x + -3x] Combine like terms: -5 + 3 = -2 -19 + 2x = 45 + -18x + -1[-2 + 5x + -3x] Combine like terms: 5x + -3x = 2x -19 + 2x = 45 + -18x + -1[-2 + 2x] -19 + 2x = 45 + -18x + [-2 * -1 + 2x * -1] -19 + 2x = 45 + -18x + [2 + -2x] Reorder the terms: -19 + 2x = 45 + 2 + -18x + -2x Combine like terms: 45 + 2 = 47 -19 + 2x = 47 + -18x + -2x Combine like terms: -18x + -2x = -20x -19 + 2x = 47 + -20x Solving -19 + 2x = 47 + -20x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20x' to each side of the equation. -19 + 2x + 20x = 47 + -20x + 20x Combine like terms: 2x + 20x = 22x -19 + 22x = 47 + -20x + 20x Combine like terms: -20x + 20x = 0 -19 + 22x = 47 + 0 -19 + 22x = 47 Add '19' to each side of the equation. -19 + 19 + 22x = 47 + 19 Combine like terms: -19 + 19 = 0 0 + 22x = 47 + 19 22x = 47 + 19 Combine like terms: 47 + 19 = 66 22x = 66 Divide each side by '22'. x = 3 Simplifying x = 3
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