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Simplifying 0.5(4x + 1) = 0.3(5x + -1) + 1.2 Reorder the terms: 0.5(1 + 4x) = 0.3(5x + -1) + 1.2 (1 * 0.5 + 4x * 0.5) = 0.3(5x + -1) + 1.2 (0.5 + 2x) = 0.3(5x + -1) + 1.2 Reorder the terms: 0.5 + 2x = 0.3(-1 + 5x) + 1.2 0.5 + 2x = (-1 * 0.3 + 5x * 0.3) + 1.2 0.5 + 2x = (-0.3 + 1.5x) + 1.2 Reorder the terms: 0.5 + 2x = -0.3 + 1.2 + 1.5x Combine like terms: -0.3 + 1.2 = 0.9 0.5 + 2x = 0.9 + 1.5x Solving 0.5 + 2x = 0.9 + 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. 0.5 + 2x + -1.5x = 0.9 + 1.5x + -1.5x Combine like terms: 2x + -1.5x = 0.5x 0.5 + 0.5x = 0.9 + 1.5x + -1.5x Combine like terms: 1.5x + -1.5x = 0.0 0.5 + 0.5x = 0.9 + 0.0 0.5 + 0.5x = 0.9 Add '-0.5' to each side of the equation. 0.5 + -0.5 + 0.5x = 0.9 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.5x = 0.9 + -0.5 0.5x = 0.9 + -0.5 Combine like terms: 0.9 + -0.5 = 0.4 0.5x = 0.4 Divide each side by '0.5'. x = 0.8 Simplifying x = 0.8
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