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Simplifying 0.2(x + 2) + 0.3x = 2(0.1x + 0.15) + 1 Reorder the terms: 0.2(2 + x) + 0.3x = 2(0.1x + 0.15) + 1 (2 * 0.2 + x * 0.2) + 0.3x = 2(0.1x + 0.15) + 1 (0.4 + 0.2x) + 0.3x = 2(0.1x + 0.15) + 1 Combine like terms: 0.2x + 0.3x = 0.5x 0.4 + 0.5x = 2(0.1x + 0.15) + 1 Reorder the terms: 0.4 + 0.5x = 2(0.15 + 0.1x) + 1 0.4 + 0.5x = (0.15 * 2 + 0.1x * 2) + 1 0.4 + 0.5x = (0.3 + 0.2x) + 1 Reorder the terms: 0.4 + 0.5x = 0.3 + 1 + 0.2x Combine like terms: 0.3 + 1 = 1.3 0.4 + 0.5x = 1.3 + 0.2x Solving 0.4 + 0.5x = 1.3 + 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. 0.4 + 0.5x + -0.2x = 1.3 + 0.2x + -0.2x Combine like terms: 0.5x + -0.2x = 0.3x 0.4 + 0.3x = 1.3 + 0.2x + -0.2x Combine like terms: 0.2x + -0.2x = 0.0 0.4 + 0.3x = 1.3 + 0.0 0.4 + 0.3x = 1.3 Add '-0.4' to each side of the equation. 0.4 + -0.4 + 0.3x = 1.3 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.3x = 1.3 + -0.4 0.3x = 1.3 + -0.4 Combine like terms: 1.3 + -0.4 = 0.9 0.3x = 0.9 Divide each side by '0.3'. x = 3 Simplifying x = 3
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