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Simplifying 2(r + 5) + -1(2 + 7r) = 3(1 + -2r) Reorder the terms: 2(5 + r) + -1(2 + 7r) = 3(1 + -2r) (5 * 2 + r * 2) + -1(2 + 7r) = 3(1 + -2r) (10 + 2r) + -1(2 + 7r) = 3(1 + -2r) 10 + 2r + (2 * -1 + 7r * -1) = 3(1 + -2r) 10 + 2r + (-2 + -7r) = 3(1 + -2r) Reorder the terms: 10 + -2 + 2r + -7r = 3(1 + -2r) Combine like terms: 10 + -2 = 8 8 + 2r + -7r = 3(1 + -2r) Combine like terms: 2r + -7r = -5r 8 + -5r = 3(1 + -2r) 8 + -5r = (1 * 3 + -2r * 3) 8 + -5r = (3 + -6r) Solving 8 + -5r = 3 + -6r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6r' to each side of the equation. 8 + -5r + 6r = 3 + -6r + 6r Combine like terms: -5r + 6r = 1r 8 + 1r = 3 + -6r + 6r Combine like terms: -6r + 6r = 0 8 + 1r = 3 + 0 8 + 1r = 3 Add '-8' to each side of the equation. 8 + -8 + 1r = 3 + -8 Combine like terms: 8 + -8 = 0 0 + 1r = 3 + -8 1r = 3 + -8 Combine like terms: 3 + -8 = -5 1r = -5 Divide each side by '1'. r = -5 Simplifying r = -5
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