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Simplifying 0.5(x + 2) + 0.75(x + 4) = x + 5 Reorder the terms: 0.5(2 + x) + 0.75(x + 4) = x + 5 (2 * 0.5 + x * 0.5) + 0.75(x + 4) = x + 5 (1 + 0.5x) + 0.75(x + 4) = x + 5 Reorder the terms: 1 + 0.5x + 0.75(4 + x) = x + 5 1 + 0.5x + (4 * 0.75 + x * 0.75) = x + 5 1 + 0.5x + (3 + 0.75x) = x + 5 Reorder the terms: 1 + 3 + 0.5x + 0.75x = x + 5 Combine like terms: 1 + 3 = 4 4 + 0.5x + 0.75x = x + 5 Combine like terms: 0.5x + 0.75x = 1.25x 4 + 1.25x = x + 5 Reorder the terms: 4 + 1.25x = 5 + x Solving 4 + 1.25x = 5 + x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 4 + 1.25x + -1x = 5 + x + -1x Combine like terms: 1.25x + -1x = 0.25x 4 + 0.25x = 5 + x + -1x Combine like terms: x + -1x = 0 4 + 0.25x = 5 + 0 4 + 0.25x = 5 Add '-4' to each side of the equation. 4 + -4 + 0.25x = 5 + -4 Combine like terms: 4 + -4 = 0 0 + 0.25x = 5 + -4 0.25x = 5 + -4 Combine like terms: 5 + -4 = 1 0.25x = 1 Divide each side by '0.25'. x = 4 Simplifying x = 4
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