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Simplifying 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20) Reorder the terms: 0.75(40 + x) = 0.35(x + 20) + 0.35(x + 20) (40 * 0.75 + x * 0.75) = 0.35(x + 20) + 0.35(x + 20) (30 + 0.75x) = 0.35(x + 20) + 0.35(x + 20) Reorder the terms: 30 + 0.75x = 0.35(20 + x) + 0.35(x + 20) 30 + 0.75x = (20 * 0.35 + x * 0.35) + 0.35(x + 20) 30 + 0.75x = (7 + 0.35x) + 0.35(x + 20) Reorder the terms: 30 + 0.75x = 7 + 0.35x + 0.35(20 + x) 30 + 0.75x = 7 + 0.35x + (20 * 0.35 + x * 0.35) 30 + 0.75x = 7 + 0.35x + (7 + 0.35x) Reorder the terms: 30 + 0.75x = 7 + 7 + 0.35x + 0.35x Combine like terms: 7 + 7 = 14 30 + 0.75x = 14 + 0.35x + 0.35x Combine like terms: 0.35x + 0.35x = 0.7x 30 + 0.75x = 14 + 0.7x Solving 30 + 0.75x = 14 + 0.7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7x' to each side of the equation. 30 + 0.75x + -0.7x = 14 + 0.7x + -0.7x Combine like terms: 0.75x + -0.7x = 0.05x 30 + 0.05x = 14 + 0.7x + -0.7x Combine like terms: 0.7x + -0.7x = 0.0 30 + 0.05x = 14 + 0.0 30 + 0.05x = 14 Add '-30' to each side of the equation. 30 + -30 + 0.05x = 14 + -30 Combine like terms: 30 + -30 = 0 0 + 0.05x = 14 + -30 0.05x = 14 + -30 Combine like terms: 14 + -30 = -16 0.05x = -16 Divide each side by '0.05'. x = -320 Simplifying x = -320
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