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Simplifying 2(x + -1) + -2(6 + -1x) = 31(2 + x) + 5 Reorder the terms: 2(-1 + x) + -2(6 + -1x) = 31(2 + x) + 5 (-1 * 2 + x * 2) + -2(6 + -1x) = 31(2 + x) + 5 (-2 + 2x) + -2(6 + -1x) = 31(2 + x) + 5 -2 + 2x + (6 * -2 + -1x * -2) = 31(2 + x) + 5 -2 + 2x + (-12 + 2x) = 31(2 + x) + 5 Reorder the terms: -2 + -12 + 2x + 2x = 31(2 + x) + 5 Combine like terms: -2 + -12 = -14 -14 + 2x + 2x = 31(2 + x) + 5 Combine like terms: 2x + 2x = 4x -14 + 4x = 31(2 + x) + 5 -14 + 4x = (2 * 31 + x * 31) + 5 -14 + 4x = (62 + 31x) + 5 Reorder the terms: -14 + 4x = 62 + 5 + 31x Combine like terms: 62 + 5 = 67 -14 + 4x = 67 + 31x Solving -14 + 4x = 67 + 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. -14 + 4x + -31x = 67 + 31x + -31x Combine like terms: 4x + -31x = -27x -14 + -27x = 67 + 31x + -31x Combine like terms: 31x + -31x = 0 -14 + -27x = 67 + 0 -14 + -27x = 67 Add '14' to each side of the equation. -14 + 14 + -27x = 67 + 14 Combine like terms: -14 + 14 = 0 0 + -27x = 67 + 14 -27x = 67 + 14 Combine like terms: 67 + 14 = 81 -27x = 81 Divide each side by '-27'. x = -3 Simplifying x = -3
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