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Simplifying 0.2(5 + -1h) + -0.5(3 + -2h) = 0.5h + 1 (5 * 0.2 + -1h * 0.2) + -0.5(3 + -2h) = 0.5h + 1 (1 + -0.2h) + -0.5(3 + -2h) = 0.5h + 1 1 + -0.2h + (3 * -0.5 + -2h * -0.5) = 0.5h + 1 1 + -0.2h + (-1.5 + 1h) = 0.5h + 1 Reorder the terms: 1 + -1.5 + -0.2h + 1h = 0.5h + 1 Combine like terms: 1 + -1.5 = -0.5 -0.5 + -0.2h + 1h = 0.5h + 1 Combine like terms: -0.2h + 1h = 0.8h -0.5 + 0.8h = 0.5h + 1 Reorder the terms: -0.5 + 0.8h = 1 + 0.5h Solving -0.5 + 0.8h = 1 + 0.5h Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.5h' to each side of the equation. -0.5 + 0.8h + -0.5h = 1 + 0.5h + -0.5h Combine like terms: 0.8h + -0.5h = 0.3h -0.5 + 0.3h = 1 + 0.5h + -0.5h Combine like terms: 0.5h + -0.5h = 0.0 -0.5 + 0.3h = 1 + 0.0 -0.5 + 0.3h = 1 Add '0.5' to each side of the equation. -0.5 + 0.5 + 0.3h = 1 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.3h = 1 + 0.5 0.3h = 1 + 0.5 Combine like terms: 1 + 0.5 = 1.5 0.3h = 1.5 Divide each side by '0.3'. h = 5 Simplifying h = 5
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