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Simplifying 5(x + 1) + 6(x + 2) = 9(x + 13) Reorder the terms: 5(1 + x) + 6(x + 2) = 9(x + 13) (1 * 5 + x * 5) + 6(x + 2) = 9(x + 13) (5 + 5x) + 6(x + 2) = 9(x + 13) Reorder the terms: 5 + 5x + 6(2 + x) = 9(x + 13) 5 + 5x + (2 * 6 + x * 6) = 9(x + 13) 5 + 5x + (12 + 6x) = 9(x + 13) Reorder the terms: 5 + 12 + 5x + 6x = 9(x + 13) Combine like terms: 5 + 12 = 17 17 + 5x + 6x = 9(x + 13) Combine like terms: 5x + 6x = 11x 17 + 11x = 9(x + 13) Reorder the terms: 17 + 11x = 9(13 + x) 17 + 11x = (13 * 9 + x * 9) 17 + 11x = (117 + 9x) Solving 17 + 11x = 117 + 9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9x' to each side of the equation. 17 + 11x + -9x = 117 + 9x + -9x Combine like terms: 11x + -9x = 2x 17 + 2x = 117 + 9x + -9x Combine like terms: 9x + -9x = 0 17 + 2x = 117 + 0 17 + 2x = 117 Add '-17' to each side of the equation. 17 + -17 + 2x = 117 + -17 Combine like terms: 17 + -17 = 0 0 + 2x = 117 + -17 2x = 117 + -17 Combine like terms: 117 + -17 = 100 2x = 100 Divide each side by '2'. x = 50 Simplifying x = 50
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