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Simplifying 9x + -1(3x + 5) + -1[8x + -1(x + 3)] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Reorder the terms: 9x + -1(5 + 3x) + -1[8x + -1(x + 3)] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] 9x + (5 * -1 + 3x * -1) + -1[8x + -1(x + 3)] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] 9x + (-5 + -3x) + -1[8x + -1(x + 3)] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Reorder the terms: 9x + -5 + -3x + -1[8x + -1(3 + x)] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] 9x + -5 + -3x + -1[8x + (3 * -1 + x * -1)] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] 9x + -5 + -3x + -1[8x + (-3 + -1x)] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Reorder the terms: 9x + -5 + -3x + -1[-3 + 8x + -1x] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Combine like terms: 8x + -1x = 7x 9x + -5 + -3x + -1[-3 + 7x] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] 9x + -5 + -3x + [-3 * -1 + 7x * -1] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] 9x + -5 + -3x + [3 + -7x] = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Reorder the terms: -5 + 3 + 9x + -3x + -7x = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Combine like terms: -5 + 3 = -2 -2 + 9x + -3x + -7x = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Combine like terms: 9x + -3x = 6x -2 + 6x + -7x = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Combine like terms: 6x + -7x = -1x -2 + -1x = 12 + -1(x + 4) + -1[3x + -2 + -1(5x + 2)] Reorder the terms: -2 + -1x = 12 + -1(4 + x) + -1[3x + -2 + -1(5x + 2)] -2 + -1x = 12 + (4 * -1 + x * -1) + -1[3x + -2 + -1(5x + 2)] -2 + -1x = 12 + (-4 + -1x) + -1[3x + -2 + -1(5x + 2)] Reorder the terms: -2 + -1x = 12 + -4 + -1x + -1[3x + -2 + -1(2 + 5x)] -2 + -1x = 12 + -4 + -1x + -1[3x + -2 + (2 * -1 + 5x * -1)] -2 + -1x = 12 + -4 + -1x + -1[3x + -2 + (-2 + -5x)] Reorder the terms: -2 + -1x = 12 + -4 + -1x + -1[-2 + -2 + 3x + -5x] Combine like terms: -2 + -2 = -4 -2 + -1x = 12 + -4 + -1x + -1[-4 + 3x + -5x] Combine like terms: 3x + -5x = -2x -2 + -1x = 12 + -4 + -1x + -1[-4 + -2x] -2 + -1x = 12 + -4 + -1x + [-4 * -1 + -2x * -1] -2 + -1x = 12 + -4 + -1x + [4 + 2x] Reorder the terms: -2 + -1x = 12 + -4 + 4 + -1x + 2x Combine like terms: 12 + -4 = 8 -2 + -1x = 8 + 4 + -1x + 2x Combine like terms: 8 + 4 = 12 -2 + -1x = 12 + -1x + 2x Combine like terms: -1x + 2x = 1x -2 + -1x = 12 + 1x Solving -2 + -1x = 12 + 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. -2 + -1x + -1x = 12 + 1x + -1x Combine like terms: -1x + -1x = -2x -2 + -2x = 12 + 1x + -1x Combine like terms: 1x + -1x = 0 -2 + -2x = 12 + 0 -2 + -2x = 12 Add '2' to each side of the equation. -2 + 2 + -2x = 12 + 2 Combine like terms: -2 + 2 = 0 0 + -2x = 12 + 2 -2x = 12 + 2 Combine like terms: 12 + 2 = 14 -2x = 14 Divide each side by '-2'. x = -7 Simplifying x = -7
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