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Simplifying 3r + 2(1 + -1r) = 2r + 10(1 + -1r) 3r + (1 * 2 + -1r * 2) = 2r + 10(1 + -1r) 3r + (2 + -2r) = 2r + 10(1 + -1r) Reorder the terms: 2 + 3r + -2r = 2r + 10(1 + -1r) Combine like terms: 3r + -2r = 1r 2 + 1r = 2r + 10(1 + -1r) 2 + 1r = 2r + (1 * 10 + -1r * 10) 2 + 1r = 2r + (10 + -10r) Reorder the terms: 2 + 1r = 10 + 2r + -10r Combine like terms: 2r + -10r = -8r 2 + 1r = 10 + -8r Solving 2 + 1r = 10 + -8r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8r' to each side of the equation. 2 + 1r + 8r = 10 + -8r + 8r Combine like terms: 1r + 8r = 9r 2 + 9r = 10 + -8r + 8r Combine like terms: -8r + 8r = 0 2 + 9r = 10 + 0 2 + 9r = 10 Add '-2' to each side of the equation. 2 + -2 + 9r = 10 + -2 Combine like terms: 2 + -2 = 0 0 + 9r = 10 + -2 9r = 10 + -2 Combine like terms: 10 + -2 = 8 9r = 8 Divide each side by '9'. r = 0.8888888889 Simplifying r = 0.8888888889
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