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Simplifying 9(x + 5) = 2(x + -7) + 5(x + 9) Reorder the terms: 9(5 + x) = 2(x + -7) + 5(x + 9) (5 * 9 + x * 9) = 2(x + -7) + 5(x + 9) (45 + 9x) = 2(x + -7) + 5(x + 9) Reorder the terms: 45 + 9x = 2(-7 + x) + 5(x + 9) 45 + 9x = (-7 * 2 + x * 2) + 5(x + 9) 45 + 9x = (-14 + 2x) + 5(x + 9) Reorder the terms: 45 + 9x = -14 + 2x + 5(9 + x) 45 + 9x = -14 + 2x + (9 * 5 + x * 5) 45 + 9x = -14 + 2x + (45 + 5x) Reorder the terms: 45 + 9x = -14 + 45 + 2x + 5x Combine like terms: -14 + 45 = 31 45 + 9x = 31 + 2x + 5x Combine like terms: 2x + 5x = 7x 45 + 9x = 31 + 7x Solving 45 + 9x = 31 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 45 + 9x + -7x = 31 + 7x + -7x Combine like terms: 9x + -7x = 2x 45 + 2x = 31 + 7x + -7x Combine like terms: 7x + -7x = 0 45 + 2x = 31 + 0 45 + 2x = 31 Add '-45' to each side of the equation. 45 + -45 + 2x = 31 + -45 Combine like terms: 45 + -45 = 0 0 + 2x = 31 + -45 2x = 31 + -45 Combine like terms: 31 + -45 = -14 2x = -14 Divide each side by '2'. x = -7 Simplifying x = -7
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