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Simplifying 4[x + -1(2x + -3)] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] Reorder the terms: 4[x + -1(-3 + 2x)] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] 4[x + (-3 * -1 + 2x * -1)] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] 4[x + (3 + -2x)] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] Reorder the terms: 4[3 + x + -2x] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] Combine like terms: x + -2x = -1x 4[3 + -1x] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] [3 * 4 + -1x * 4] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] [12 + -4x] + -3(2x + 9) = 46 + -1[3(6 + -1x) + -4(7x + 20)] Reorder the terms: 12 + -4x + -3(9 + 2x) = 46 + -1[3(6 + -1x) + -4(7x + 20)] 12 + -4x + (9 * -3 + 2x * -3) = 46 + -1[3(6 + -1x) + -4(7x + 20)] 12 + -4x + (-27 + -6x) = 46 + -1[3(6 + -1x) + -4(7x + 20)] Reorder the terms: 12 + -27 + -4x + -6x = 46 + -1[3(6 + -1x) + -4(7x + 20)] Combine like terms: 12 + -27 = -15 -15 + -4x + -6x = 46 + -1[3(6 + -1x) + -4(7x + 20)] Combine like terms: -4x + -6x = -10x -15 + -10x = 46 + -1[3(6 + -1x) + -4(7x + 20)] -15 + -10x = 46 + -1[(6 * 3 + -1x * 3) + -4(7x + 20)] -15 + -10x = 46 + -1[(18 + -3x) + -4(7x + 20)] Reorder the terms: -15 + -10x = 46 + -1[18 + -3x + -4(20 + 7x)] -15 + -10x = 46 + -1[18 + -3x + (20 * -4 + 7x * -4)] -15 + -10x = 46 + -1[18 + -3x + (-80 + -28x)] Reorder the terms: -15 + -10x = 46 + -1[18 + -80 + -3x + -28x] Combine like terms: 18 + -80 = -62 -15 + -10x = 46 + -1[-62 + -3x + -28x] Combine like terms: -3x + -28x = -31x -15 + -10x = 46 + -1[-62 + -31x] -15 + -10x = 46 + [-62 * -1 + -31x * -1] -15 + -10x = 46 + [62 + 31x] Combine like terms: 46 + 62 = 108 -15 + -10x = 108 + 31x Solving -15 + -10x = 108 + 31x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31x' to each side of the equation. -15 + -10x + -31x = 108 + 31x + -31x Combine like terms: -10x + -31x = -41x -15 + -41x = 108 + 31x + -31x Combine like terms: 31x + -31x = 0 -15 + -41x = 108 + 0 -15 + -41x = 108 Add '15' to each side of the equation. -15 + 15 + -41x = 108 + 15 Combine like terms: -15 + 15 = 0 0 + -41x = 108 + 15 -41x = 108 + 15 Combine like terms: 108 + 15 = 123 -41x = 123 Divide each side by '-41'. x = -3 Simplifying x = -3
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