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Simplifying 7(r + 6) = 5(r + 8) Reorder the terms: 7(6 + r) = 5(r + 8) (6 * 7 + r * 7) = 5(r + 8) (42 + 7r) = 5(r + 8) Reorder the terms: 42 + 7r = 5(8 + r) 42 + 7r = (8 * 5 + r * 5) 42 + 7r = (40 + 5r) Solving 42 + 7r = 40 + 5r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5r' to each side of the equation. 42 + 7r + -5r = 40 + 5r + -5r Combine like terms: 7r + -5r = 2r 42 + 2r = 40 + 5r + -5r Combine like terms: 5r + -5r = 0 42 + 2r = 40 + 0 42 + 2r = 40 Add '-42' to each side of the equation. 42 + -42 + 2r = 40 + -42 Combine like terms: 42 + -42 = 0 0 + 2r = 40 + -42 2r = 40 + -42 Combine like terms: 40 + -42 = -2 2r = -2 Divide each side by '2'. r = -1 Simplifying r = -1
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