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Simplifying 0.7x + 0.2(1 + -1x) = 0.1x + 0.4(1 + -1x) 0.7x + (1 * 0.2 + -1x * 0.2) = 0.1x + 0.4(1 + -1x) 0.7x + (0.2 + -0.2x) = 0.1x + 0.4(1 + -1x) Reorder the terms: 0.2 + 0.7x + -0.2x = 0.1x + 0.4(1 + -1x) Combine like terms: 0.7x + -0.2x = 0.5x 0.2 + 0.5x = 0.1x + 0.4(1 + -1x) 0.2 + 0.5x = 0.1x + (1 * 0.4 + -1x * 0.4) 0.2 + 0.5x = 0.1x + (0.4 + -0.4x) Reorder the terms: 0.2 + 0.5x = 0.4 + 0.1x + -0.4x Combine like terms: 0.1x + -0.4x = -0.3x 0.2 + 0.5x = 0.4 + -0.3x Solving 0.2 + 0.5x = 0.4 + -0.3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3x' to each side of the equation. 0.2 + 0.5x + 0.3x = 0.4 + -0.3x + 0.3x Combine like terms: 0.5x + 0.3x = 0.8x 0.2 + 0.8x = 0.4 + -0.3x + 0.3x Combine like terms: -0.3x + 0.3x = 0.0 0.2 + 0.8x = 0.4 + 0.0 0.2 + 0.8x = 0.4 Add '-0.2' to each side of the equation. 0.2 + -0.2 + 0.8x = 0.4 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.8x = 0.4 + -0.2 0.8x = 0.4 + -0.2 Combine like terms: 0.4 + -0.2 = 0.2 0.8x = 0.2 Divide each side by '0.8'. x = 0.25 Simplifying x = 0.25
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