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Simplifying 21x + -1[9 + -1(5x + -6) + 8x] = 15 + -1[(4x + -7) + -1(6x + -5)] Reorder the terms: 21x + -1[9 + -1(-6 + 5x) + 8x] = 15 + -1[(4x + -7) + -1(6x + -5)] 21x + -1[9 + (-6 * -1 + 5x * -1) + 8x] = 15 + -1[(4x + -7) + -1(6x + -5)] 21x + -1[9 + (6 + -5x) + 8x] = 15 + -1[(4x + -7) + -1(6x + -5)] Combine like terms: 9 + 6 = 15 21x + -1[15 + -5x + 8x] = 15 + -1[(4x + -7) + -1(6x + -5)] Combine like terms: -5x + 8x = 3x 21x + -1[15 + 3x] = 15 + -1[(4x + -7) + -1(6x + -5)] 21x + [15 * -1 + 3x * -1] = 15 + -1[(4x + -7) + -1(6x + -5)] 21x + [-15 + -3x] = 15 + -1[(4x + -7) + -1(6x + -5)] Reorder the terms: -15 + 21x + -3x = 15 + -1[(4x + -7) + -1(6x + -5)] Combine like terms: 21x + -3x = 18x -15 + 18x = 15 + -1[(4x + -7) + -1(6x + -5)] Reorder the terms: -15 + 18x = 15 + -1[(-7 + 4x) + -1(6x + -5)] Remove parenthesis around (-7 + 4x) -15 + 18x = 15 + -1[-7 + 4x + -1(6x + -5)] Reorder the terms: -15 + 18x = 15 + -1[-7 + 4x + -1(-5 + 6x)] -15 + 18x = 15 + -1[-7 + 4x + (-5 * -1 + 6x * -1)] -15 + 18x = 15 + -1[-7 + 4x + (5 + -6x)] Reorder the terms: -15 + 18x = 15 + -1[-7 + 5 + 4x + -6x] Combine like terms: -7 + 5 = -2 -15 + 18x = 15 + -1[-2 + 4x + -6x] Combine like terms: 4x + -6x = -2x -15 + 18x = 15 + -1[-2 + -2x] -15 + 18x = 15 + [-2 * -1 + -2x * -1] -15 + 18x = 15 + [2 + 2x] Combine like terms: 15 + 2 = 17 -15 + 18x = 17 + 2x Solving -15 + 18x = 17 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -15 + 18x + -2x = 17 + 2x + -2x Combine like terms: 18x + -2x = 16x -15 + 16x = 17 + 2x + -2x Combine like terms: 2x + -2x = 0 -15 + 16x = 17 + 0 -15 + 16x = 17 Add '15' to each side of the equation. -15 + 15 + 16x = 17 + 15 Combine like terms: -15 + 15 = 0 0 + 16x = 17 + 15 16x = 17 + 15 Combine like terms: 17 + 15 = 32 16x = 32 Divide each side by '16'. x = 2 Simplifying x = 2
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