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Simplifying 0.5(x + -2) = 1 + -1(0.2x + 1) Reorder the terms: 0.5(-2 + x) = 1 + -1(0.2x + 1) (-2 * 0.5 + x * 0.5) = 1 + -1(0.2x + 1) (-1 + 0.5x) = 1 + -1(0.2x + 1) Reorder the terms: -1 + 0.5x = 1 + -1(1 + 0.2x) -1 + 0.5x = 1 + (1 * -1 + 0.2x * -1) -1 + 0.5x = 1 + (-1 + -0.2x) Combine like terms: 1 + -1 = 0 -1 + 0.5x = 0 + -0.2x -1 + 0.5x = -0.2x Solving -1 + 0.5x = -0.2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2x' to each side of the equation. -1 + 0.5x + 0.2x = -0.2x + 0.2x Combine like terms: 0.5x + 0.2x = 0.7x -1 + 0.7x = -0.2x + 0.2x Combine like terms: -0.2x + 0.2x = 0.0 -1 + 0.7x = 0.0 Add '1' to each side of the equation. -1 + 1 + 0.7x = 0.0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.7x = 0.0 + 1 0.7x = 0.0 + 1 Combine like terms: 0.0 + 1 = 1 0.7x = 1 Divide each side by '0.7'. x = 1.428571429 Simplifying x = 1.428571429
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