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Simplifying 0.5(x + 15) + 0.4(x + 25) = 31 Reorder the terms: 0.5(15 + x) + 0.4(x + 25) = 31 (15 * 0.5 + x * 0.5) + 0.4(x + 25) = 31 (7.5 + 0.5x) + 0.4(x + 25) = 31 Reorder the terms: 7.5 + 0.5x + 0.4(25 + x) = 31 7.5 + 0.5x + (25 * 0.4 + x * 0.4) = 31 7.5 + 0.5x + (10 + 0.4x) = 31 Reorder the terms: 7.5 + 10 + 0.5x + 0.4x = 31 Combine like terms: 7.5 + 10 = 17.5 17.5 + 0.5x + 0.4x = 31 Combine like terms: 0.5x + 0.4x = 0.9x 17.5 + 0.9x = 31 Solving 17.5 + 0.9x = 31 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + 0.9x = 31 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + 0.9x = 31 + -17.5 0.9x = 31 + -17.5 Combine like terms: 31 + -17.5 = 13.5 0.9x = 13.5 Divide each side by '0.9'. x = 15 Simplifying x = 15
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