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Simplifying 5(x + 9) + 3(3x + -1) = 13(x + 1) + 9 Reorder the terms: 5(9 + x) + 3(3x + -1) = 13(x + 1) + 9 (9 * 5 + x * 5) + 3(3x + -1) = 13(x + 1) + 9 (45 + 5x) + 3(3x + -1) = 13(x + 1) + 9 Reorder the terms: 45 + 5x + 3(-1 + 3x) = 13(x + 1) + 9 45 + 5x + (-1 * 3 + 3x * 3) = 13(x + 1) + 9 45 + 5x + (-3 + 9x) = 13(x + 1) + 9 Reorder the terms: 45 + -3 + 5x + 9x = 13(x + 1) + 9 Combine like terms: 45 + -3 = 42 42 + 5x + 9x = 13(x + 1) + 9 Combine like terms: 5x + 9x = 14x 42 + 14x = 13(x + 1) + 9 Reorder the terms: 42 + 14x = 13(1 + x) + 9 42 + 14x = (1 * 13 + x * 13) + 9 42 + 14x = (13 + 13x) + 9 Reorder the terms: 42 + 14x = 13 + 9 + 13x Combine like terms: 13 + 9 = 22 42 + 14x = 22 + 13x Solving 42 + 14x = 22 + 13x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13x' to each side of the equation. 42 + 14x + -13x = 22 + 13x + -13x Combine like terms: 14x + -13x = 1x 42 + 1x = 22 + 13x + -13x Combine like terms: 13x + -13x = 0 42 + 1x = 22 + 0 42 + 1x = 22 Add '-42' to each side of the equation. 42 + -42 + 1x = 22 + -42 Combine like terms: 42 + -42 = 0 0 + 1x = 22 + -42 1x = 22 + -42 Combine like terms: 22 + -42 = -20 1x = -20 Divide each side by '1'. x = -20 Simplifying x = -20
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