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Simplifying 3x + -8(3x + -4) = 31 + 6(1 + -6x) + -2(3 + -8x) Reorder the terms: 3x + -8(-4 + 3x) = 31 + 6(1 + -6x) + -2(3 + -8x) 3x + (-4 * -8 + 3x * -8) = 31 + 6(1 + -6x) + -2(3 + -8x) 3x + (32 + -24x) = 31 + 6(1 + -6x) + -2(3 + -8x) Reorder the terms: 32 + 3x + -24x = 31 + 6(1 + -6x) + -2(3 + -8x) Combine like terms: 3x + -24x = -21x 32 + -21x = 31 + 6(1 + -6x) + -2(3 + -8x) 32 + -21x = 31 + (1 * 6 + -6x * 6) + -2(3 + -8x) 32 + -21x = 31 + (6 + -36x) + -2(3 + -8x) 32 + -21x = 31 + 6 + -36x + (3 * -2 + -8x * -2) 32 + -21x = 31 + 6 + -36x + (-6 + 16x) Reorder the terms: 32 + -21x = 31 + 6 + -6 + -36x + 16x Combine like terms: 31 + 6 = 37 32 + -21x = 37 + -6 + -36x + 16x Combine like terms: 37 + -6 = 31 32 + -21x = 31 + -36x + 16x Combine like terms: -36x + 16x = -20x 32 + -21x = 31 + -20x Solving 32 + -21x = 31 + -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. 32 + -21x + 20x = 31 + -20x + 20x Combine like terms: -21x + 20x = -1x 32 + -1x = 31 + -20x + 20x Combine like terms: -20x + 20x = 0 32 + -1x = 31 + 0 32 + -1x = 31 Add '-32' to each side of the equation. 32 + -32 + -1x = 31 + -32 Combine like terms: 32 + -32 = 0 0 + -1x = 31 + -32 -1x = 31 + -32 Combine like terms: 31 + -32 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1
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