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Simplifying 3(1 + x) = 2[3(x + 2) + -1(x + -1)] (1 * 3 + x * 3) = 2[3(x + 2) + -1(x + -1)] (3 + 3x) = 2[3(x + 2) + -1(x + -1)] Reorder the terms: 3 + 3x = 2[3(2 + x) + -1(x + -1)] 3 + 3x = 2[(2 * 3 + x * 3) + -1(x + -1)] 3 + 3x = 2[(6 + 3x) + -1(x + -1)] Reorder the terms: 3 + 3x = 2[6 + 3x + -1(-1 + x)] 3 + 3x = 2[6 + 3x + (-1 * -1 + x * -1)] 3 + 3x = 2[6 + 3x + (1 + -1x)] Reorder the terms: 3 + 3x = 2[6 + 1 + 3x + -1x] Combine like terms: 6 + 1 = 7 3 + 3x = 2[7 + 3x + -1x] Combine like terms: 3x + -1x = 2x 3 + 3x = 2[7 + 2x] 3 + 3x = [7 * 2 + 2x * 2] 3 + 3x = [14 + 4x] Solving 3 + 3x = 14 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 3 + 3x + -4x = 14 + 4x + -4x Combine like terms: 3x + -4x = -1x 3 + -1x = 14 + 4x + -4x Combine like terms: 4x + -4x = 0 3 + -1x = 14 + 0 3 + -1x = 14 Add '-3' to each side of the equation. 3 + -3 + -1x = 14 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 14 + -3 -1x = 14 + -3 Combine like terms: 14 + -3 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11
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