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Simplifying 0.5(4x + -5) + 2x = 3.2(x + 2) + -3.82 Reorder the terms: 0.5(-5 + 4x) + 2x = 3.2(x + 2) + -3.82 (-5 * 0.5 + 4x * 0.5) + 2x = 3.2(x + 2) + -3.82 (-2.5 + 2x) + 2x = 3.2(x + 2) + -3.82 Combine like terms: 2x + 2x = 4x -2.5 + 4x = 3.2(x + 2) + -3.82 Reorder the terms: -2.5 + 4x = 3.2(2 + x) + -3.82 -2.5 + 4x = (2 * 3.2 + x * 3.2) + -3.82 -2.5 + 4x = (6.4 + 3.2x) + -3.82 Reorder the terms: -2.5 + 4x = 6.4 + -3.82 + 3.2x Combine like terms: 6.4 + -3.82 = 2.58 -2.5 + 4x = 2.58 + 3.2x Solving -2.5 + 4x = 2.58 + 3.2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2x' to each side of the equation. -2.5 + 4x + -3.2x = 2.58 + 3.2x + -3.2x Combine like terms: 4x + -3.2x = 0.8x -2.5 + 0.8x = 2.58 + 3.2x + -3.2x Combine like terms: 3.2x + -3.2x = 0.0 -2.5 + 0.8x = 2.58 + 0.0 -2.5 + 0.8x = 2.58 Add '2.5' to each side of the equation. -2.5 + 2.5 + 0.8x = 2.58 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.8x = 2.58 + 2.5 0.8x = 2.58 + 2.5 Combine like terms: 2.58 + 2.5 = 5.08 0.8x = 5.08 Divide each side by '0.8'. x = 6.35 Simplifying x = 6.35
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