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Simplifying 3(1 + x) = 2[5(x + 3) + -1(x + 1)] (1 * 3 + x * 3) = 2[5(x + 3) + -1(x + 1)] (3 + 3x) = 2[5(x + 3) + -1(x + 1)] Reorder the terms: 3 + 3x = 2[5(3 + x) + -1(x + 1)] 3 + 3x = 2[(3 * 5 + x * 5) + -1(x + 1)] 3 + 3x = 2[(15 + 5x) + -1(x + 1)] Reorder the terms: 3 + 3x = 2[15 + 5x + -1(1 + x)] 3 + 3x = 2[15 + 5x + (1 * -1 + x * -1)] 3 + 3x = 2[15 + 5x + (-1 + -1x)] Reorder the terms: 3 + 3x = 2[15 + -1 + 5x + -1x] Combine like terms: 15 + -1 = 14 3 + 3x = 2[14 + 5x + -1x] Combine like terms: 5x + -1x = 4x 3 + 3x = 2[14 + 4x] 3 + 3x = [14 * 2 + 4x * 2] 3 + 3x = [28 + 8x] Solving 3 + 3x = 28 + 8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. 3 + 3x + -8x = 28 + 8x + -8x Combine like terms: 3x + -8x = -5x 3 + -5x = 28 + 8x + -8x Combine like terms: 8x + -8x = 0 3 + -5x = 28 + 0 3 + -5x = 28 Add '-3' to each side of the equation. 3 + -3 + -5x = 28 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 28 + -3 -5x = 28 + -3 Combine like terms: 28 + -3 = 25 -5x = 25 Divide each side by '-5'. x = -5 Simplifying x = -5
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