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Simplifying 3(1 + 2r) + 5r = 7(1 + 2r) + 5 (1 * 3 + 2r * 3) + 5r = 7(1 + 2r) + 5 (3 + 6r) + 5r = 7(1 + 2r) + 5 Combine like terms: 6r + 5r = 11r 3 + 11r = 7(1 + 2r) + 5 3 + 11r = (1 * 7 + 2r * 7) + 5 3 + 11r = (7 + 14r) + 5 Reorder the terms: 3 + 11r = 7 + 5 + 14r Combine like terms: 7 + 5 = 12 3 + 11r = 12 + 14r Solving 3 + 11r = 12 + 14r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-14r' to each side of the equation. 3 + 11r + -14r = 12 + 14r + -14r Combine like terms: 11r + -14r = -3r 3 + -3r = 12 + 14r + -14r Combine like terms: 14r + -14r = 0 3 + -3r = 12 + 0 3 + -3r = 12 Add '-3' to each side of the equation. 3 + -3 + -3r = 12 + -3 Combine like terms: 3 + -3 = 0 0 + -3r = 12 + -3 -3r = 12 + -3 Combine like terms: 12 + -3 = 9 -3r = 9 Divide each side by '-3'. r = -3 Simplifying r = -3
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