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Simplifying 0.7x + 0.1(1 + -1x) = 0.2x + 0.4(1 + -1x) 0.7x + (1 * 0.1 + -1x * 0.1) = 0.2x + 0.4(1 + -1x) 0.7x + (0.1 + -0.1x) = 0.2x + 0.4(1 + -1x) Reorder the terms: 0.1 + 0.7x + -0.1x = 0.2x + 0.4(1 + -1x) Combine like terms: 0.7x + -0.1x = 0.6x 0.1 + 0.6x = 0.2x + 0.4(1 + -1x) 0.1 + 0.6x = 0.2x + (1 * 0.4 + -1x * 0.4) 0.1 + 0.6x = 0.2x + (0.4 + -0.4x) Reorder the terms: 0.1 + 0.6x = 0.4 + 0.2x + -0.4x Combine like terms: 0.2x + -0.4x = -0.2x 0.1 + 0.6x = 0.4 + -0.2x Solving 0.1 + 0.6x = 0.4 + -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. 0.1 + 0.6x + 0.2x = 0.4 + -0.2x + 0.2x Combine like terms: 0.6x + 0.2x = 0.8x 0.1 + 0.8x = 0.4 + -0.2x + 0.2x Combine like terms: -0.2x + 0.2x = 0.0 0.1 + 0.8x = 0.4 + 0.0 0.1 + 0.8x = 0.4 Add '-0.1' to each side of the equation. 0.1 + -0.1 + 0.8x = 0.4 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 0.8x = 0.4 + -0.1 0.8x = 0.4 + -0.1 Combine like terms: 0.4 + -0.1 = 0.3 0.8x = 0.3 Divide each side by '0.8'. x = 0.375 Simplifying x = 0.375
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