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Simplifying 0.5(4x + 1) + 2(2 + -0.5x) = (4.5 + -2.5x) Reorder the terms: 0.5(1 + 4x) + 2(2 + -0.5x) = (4.5 + -2.5x) (1 * 0.5 + 4x * 0.5) + 2(2 + -0.5x) = (4.5 + -2.5x) (0.5 + 2x) + 2(2 + -0.5x) = (4.5 + -2.5x) 0.5 + 2x + (2 * 2 + -0.5x * 2) = (4.5 + -2.5x) 0.5 + 2x + (4 + -1x) = (4.5 + -2.5x) Reorder the terms: 0.5 + 4 + 2x + -1x = (4.5 + -2.5x) Combine like terms: 0.5 + 4 = 4.5 4.5 + 2x + -1x = (4.5 + -2.5x) Combine like terms: 2x + -1x = 1x 4.5 + 1x = (4.5 + -2.5x) Remove parenthesis around (4.5 + -2.5x) 4.5 + 1x = 4.5 + -2.5x Add '-4.5' to each side of the equation. 4.5 + -4.5 + 1x = 4.5 + -4.5 + -2.5x Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 1x = 4.5 + -4.5 + -2.5x 1x = 4.5 + -4.5 + -2.5x Combine like terms: 4.5 + -4.5 = 0.0 1x = 0.0 + -2.5x 1x = -2.5x Solving 1x = -2.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5x' to each side of the equation. 1x + 2.5x = -2.5x + 2.5x Combine like terms: 1x + 2.5x = 3.5x 3.5x = -2.5x + 2.5x Combine like terms: -2.5x + 2.5x = 0.0 3.5x = 0.0 Divide each side by '3.5'. x = 0 Simplifying x = 0
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