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Simplifying 10(1 + -2r) = -5(2r + -1) (1 * 10 + -2r * 10) = -5(2r + -1) (10 + -20r) = -5(2r + -1) Reorder the terms: 10 + -20r = -5(-1 + 2r) 10 + -20r = (-1 * -5 + 2r * -5) 10 + -20r = (5 + -10r) Solving 10 + -20r = 5 + -10r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10r' to each side of the equation. 10 + -20r + 10r = 5 + -10r + 10r Combine like terms: -20r + 10r = -10r 10 + -10r = 5 + -10r + 10r Combine like terms: -10r + 10r = 0 10 + -10r = 5 + 0 10 + -10r = 5 Add '-10' to each side of the equation. 10 + -10 + -10r = 5 + -10 Combine like terms: 10 + -10 = 0 0 + -10r = 5 + -10 -10r = 5 + -10 Combine like terms: 5 + -10 = -5 -10r = -5 Divide each side by '-10'. r = 0.5 Simplifying r = 0.5
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