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Simplifying 5(r + 6) = 6(r + 7) Reorder the terms: 5(6 + r) = 6(r + 7) (6 * 5 + r * 5) = 6(r + 7) (30 + 5r) = 6(r + 7) Reorder the terms: 30 + 5r = 6(7 + r) 30 + 5r = (7 * 6 + r * 6) 30 + 5r = (42 + 6r) Solving 30 + 5r = 42 + 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. 30 + 5r + -6r = 42 + 6r + -6r Combine like terms: 5r + -6r = -1r 30 + -1r = 42 + 6r + -6r Combine like terms: 6r + -6r = 0 30 + -1r = 42 + 0 30 + -1r = 42 Add '-30' to each side of the equation. 30 + -30 + -1r = 42 + -30 Combine like terms: 30 + -30 = 0 0 + -1r = 42 + -30 -1r = 42 + -30 Combine like terms: 42 + -30 = 12 -1r = 12 Divide each side by '-1'. r = -12 Simplifying r = -12
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