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Simplifying [x + -0.2(x + -1000)] * 0.75 = 0 Reorder the terms: [x + -0.2(-1000 + x)] * 0.75 = 0 [x + (-1000 * -0.2 + x * -0.2)] * 0.75 = 0 [x + (200 + -0.2x)] * 0.75 = 0 Reorder the terms: [200 + x + -0.2x] * 0.75 = 0 Combine like terms: x + -0.2x = 0.8x [200 + 0.8x] * 0.75 = 0 Reorder the terms for easier multiplication: 0.75[200 + 0.8x] = 0 [200 * 0.75 + 0.8x * 0.75] = 0 [150 + 0.6x] = 0 Solving 150 + 0.6x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + 0.6x = 0 + -150 Combine like terms: 150 + -150 = 0 0 + 0.6x = 0 + -150 0.6x = 0 + -150 Combine like terms: 0 + -150 = -150 0.6x = -150 Divide each side by '0.6'. x = -250 Simplifying x = -250
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