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Simplifying 0.5 + 2(0.75r + -1) = 0.75r + 6 Reorder the terms: 0.5 + 2(-1 + 0.75r) = 0.75r + 6 0.5 + (-1 * 2 + 0.75r * 2) = 0.75r + 6 0.5 + (-2 + 1.5r) = 0.75r + 6 Combine like terms: 0.5 + -2 = -1.5 -1.5 + 1.5r = 0.75r + 6 Reorder the terms: -1.5 + 1.5r = 6 + 0.75r Solving -1.5 + 1.5r = 6 + 0.75r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75r' to each side of the equation. -1.5 + 1.5r + -0.75r = 6 + 0.75r + -0.75r Combine like terms: 1.5r + -0.75r = 0.75r -1.5 + 0.75r = 6 + 0.75r + -0.75r Combine like terms: 0.75r + -0.75r = 0.00 -1.5 + 0.75r = 6 + 0.00 -1.5 + 0.75r = 6 Add '1.5' to each side of the equation. -1.5 + 1.5 + 0.75r = 6 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.75r = 6 + 1.5 0.75r = 6 + 1.5 Combine like terms: 6 + 1.5 = 7.5 0.75r = 7.5 Divide each side by '0.75'. r = 10 Simplifying r = 10
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