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Simplifying 250 + -0.3(x + 100) = 0.5(600 + -1x) + -40 Reorder the terms: 250 + -0.3(100 + x) = 0.5(600 + -1x) + -40 250 + (100 * -0.3 + x * -0.3) = 0.5(600 + -1x) + -40 250 + (-30 + -0.3x) = 0.5(600 + -1x) + -40 Combine like terms: 250 + -30 = 220 220 + -0.3x = 0.5(600 + -1x) + -40 220 + -0.3x = (600 * 0.5 + -1x * 0.5) + -40 220 + -0.3x = (300 + -0.5x) + -40 Reorder the terms: 220 + -0.3x = 300 + -40 + -0.5x Combine like terms: 300 + -40 = 260 220 + -0.3x = 260 + -0.5x Solving 220 + -0.3x = 260 + -0.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5x' to each side of the equation. 220 + -0.3x + 0.5x = 260 + -0.5x + 0.5x Combine like terms: -0.3x + 0.5x = 0.2x 220 + 0.2x = 260 + -0.5x + 0.5x Combine like terms: -0.5x + 0.5x = 0.0 220 + 0.2x = 260 + 0.0 220 + 0.2x = 260 Add '-220' to each side of the equation. 220 + -220 + 0.2x = 260 + -220 Combine like terms: 220 + -220 = 0 0 + 0.2x = 260 + -220 0.2x = 260 + -220 Combine like terms: 260 + -220 = 40 0.2x = 40 Divide each side by '0.2'. x = 200 Simplifying x = 200
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