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Simplifying -2[3(x + -1) + -2(4x + 3)] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] Reorder the terms: -2[3(-1 + x) + -2(4x + 3)] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] -2[(-1 * 3 + x * 3) + -2(4x + 3)] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] -2[(-3 + 3x) + -2(4x + 3)] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] Reorder the terms: -2[-3 + 3x + -2(3 + 4x)] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] -2[-3 + 3x + (3 * -2 + 4x * -2)] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] -2[-3 + 3x + (-6 + -8x)] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] Reorder the terms: -2[-3 + -6 + 3x + -8x] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] Combine like terms: -3 + -6 = -9 -2[-9 + 3x + -8x] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] Combine like terms: 3x + -8x = -5x -2[-9 + -5x] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] [-9 * -2 + -5x * -2] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] [18 + 10x] + -3(x + -1) = 5 + -1[3(2x + -1) + -4(5x + 3)] Reorder the terms: 18 + 10x + -3(-1 + x) = 5 + -1[3(2x + -1) + -4(5x + 3)] 18 + 10x + (-1 * -3 + x * -3) = 5 + -1[3(2x + -1) + -4(5x + 3)] 18 + 10x + (3 + -3x) = 5 + -1[3(2x + -1) + -4(5x + 3)] Reorder the terms: 18 + 3 + 10x + -3x = 5 + -1[3(2x + -1) + -4(5x + 3)] Combine like terms: 18 + 3 = 21 21 + 10x + -3x = 5 + -1[3(2x + -1) + -4(5x + 3)] Combine like terms: 10x + -3x = 7x 21 + 7x = 5 + -1[3(2x + -1) + -4(5x + 3)] Reorder the terms: 21 + 7x = 5 + -1[3(-1 + 2x) + -4(5x + 3)] 21 + 7x = 5 + -1[(-1 * 3 + 2x * 3) + -4(5x + 3)] 21 + 7x = 5 + -1[(-3 + 6x) + -4(5x + 3)] Reorder the terms: 21 + 7x = 5 + -1[-3 + 6x + -4(3 + 5x)] 21 + 7x = 5 + -1[-3 + 6x + (3 * -4 + 5x * -4)] 21 + 7x = 5 + -1[-3 + 6x + (-12 + -20x)] Reorder the terms: 21 + 7x = 5 + -1[-3 + -12 + 6x + -20x] Combine like terms: -3 + -12 = -15 21 + 7x = 5 + -1[-15 + 6x + -20x] Combine like terms: 6x + -20x = -14x 21 + 7x = 5 + -1[-15 + -14x] 21 + 7x = 5 + [-15 * -1 + -14x * -1] 21 + 7x = 5 + [15 + 14x] Combine like terms: 5 + 15 = 20 21 + 7x = 20 + 14x Solving 21 + 7x = 20 + 14x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14x' to each side of the equation. 21 + 7x + -14x = 20 + 14x + -14x Combine like terms: 7x + -14x = -7x 21 + -7x = 20 + 14x + -14x Combine like terms: 14x + -14x = 0 21 + -7x = 20 + 0 21 + -7x = 20 Add '-21' to each side of the equation. 21 + -21 + -7x = 20 + -21 Combine like terms: 21 + -21 = 0 0 + -7x = 20 + -21 -7x = 20 + -21 Combine like terms: 20 + -21 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429
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