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Simplifying 0.5x + 1 = (2 + -0.5x) + -1(1 + x) Reorder the terms: 1 + 0.5x = (2 + -0.5x) + -1(1 + x) Remove parenthesis around (2 + -0.5x) 1 + 0.5x = 2 + -0.5x + -1(1 + x) 1 + 0.5x = 2 + -0.5x + (1 * -1 + x * -1) 1 + 0.5x = 2 + -0.5x + (-1 + -1x) Reorder the terms: 1 + 0.5x = 2 + -1 + -0.5x + -1x Combine like terms: 2 + -1 = 1 1 + 0.5x = 1 + -0.5x + -1x Combine like terms: -0.5x + -1x = -1.5x 1 + 0.5x = 1 + -1.5x Add '-1' to each side of the equation. 1 + -1 + 0.5x = 1 + -1 + -1.5x Combine like terms: 1 + -1 = 0 0 + 0.5x = 1 + -1 + -1.5x 0.5x = 1 + -1 + -1.5x Combine like terms: 1 + -1 = 0 0.5x = 0 + -1.5x 0.5x = -1.5x Solving 0.5x = -1.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5x' to each side of the equation. 0.5x + 1.5x = -1.5x + 1.5x Combine like terms: 0.5x + 1.5x = 2x 2x = -1.5x + 1.5x Combine like terms: -1.5x + 1.5x = 0.0 2x = 0.0 Divide each side by '2'. x = 0.0 Simplifying x = 0.0
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