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Simplifying 5(2x + 3) + -1(1 + -2x) = 2[3(3 + 2x) + -1(3 + -1x)] Reorder the terms: 5(3 + 2x) + -1(1 + -2x) = 2[3(3 + 2x) + -1(3 + -1x)] (3 * 5 + 2x * 5) + -1(1 + -2x) = 2[3(3 + 2x) + -1(3 + -1x)] (15 + 10x) + -1(1 + -2x) = 2[3(3 + 2x) + -1(3 + -1x)] 15 + 10x + (1 * -1 + -2x * -1) = 2[3(3 + 2x) + -1(3 + -1x)] 15 + 10x + (-1 + 2x) = 2[3(3 + 2x) + -1(3 + -1x)] Reorder the terms: 15 + -1 + 10x + 2x = 2[3(3 + 2x) + -1(3 + -1x)] Combine like terms: 15 + -1 = 14 14 + 10x + 2x = 2[3(3 + 2x) + -1(3 + -1x)] Combine like terms: 10x + 2x = 12x 14 + 12x = 2[3(3 + 2x) + -1(3 + -1x)] 14 + 12x = 2[(3 * 3 + 2x * 3) + -1(3 + -1x)] 14 + 12x = 2[(9 + 6x) + -1(3 + -1x)] 14 + 12x = 2[9 + 6x + (3 * -1 + -1x * -1)] 14 + 12x = 2[9 + 6x + (-3 + 1x)] Reorder the terms: 14 + 12x = 2[9 + -3 + 6x + 1x] Combine like terms: 9 + -3 = 6 14 + 12x = 2[6 + 6x + 1x] Combine like terms: 6x + 1x = 7x 14 + 12x = 2[6 + 7x] 14 + 12x = [6 * 2 + 7x * 2] 14 + 12x = [12 + 14x] Solving 14 + 12x = 12 + 14x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14x' to each side of the equation. 14 + 12x + -14x = 12 + 14x + -14x Combine like terms: 12x + -14x = -2x 14 + -2x = 12 + 14x + -14x Combine like terms: 14x + -14x = 0 14 + -2x = 12 + 0 14 + -2x = 12 Add '-14' to each side of the equation. 14 + -14 + -2x = 12 + -14 Combine like terms: 14 + -14 = 0 0 + -2x = 12 + -14 -2x = 12 + -14 Combine like terms: 12 + -14 = -2 -2x = -2 Divide each side by '-2'. x = 1 Simplifying x = 1
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