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Simplifying 2 + 7(3 + 2r) = 6(2r + 8) + 1 2 + (3 * 7 + 2r * 7) = 6(2r + 8) + 1 2 + (21 + 14r) = 6(2r + 8) + 1 Combine like terms: 2 + 21 = 23 23 + 14r = 6(2r + 8) + 1 Reorder the terms: 23 + 14r = 6(8 + 2r) + 1 23 + 14r = (8 * 6 + 2r * 6) + 1 23 + 14r = (48 + 12r) + 1 Reorder the terms: 23 + 14r = 48 + 1 + 12r Combine like terms: 48 + 1 = 49 23 + 14r = 49 + 12r Solving 23 + 14r = 49 + 12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. 23 + 14r + -12r = 49 + 12r + -12r Combine like terms: 14r + -12r = 2r 23 + 2r = 49 + 12r + -12r Combine like terms: 12r + -12r = 0 23 + 2r = 49 + 0 23 + 2r = 49 Add '-23' to each side of the equation. 23 + -23 + 2r = 49 + -23 Combine like terms: 23 + -23 = 0 0 + 2r = 49 + -23 2r = 49 + -23 Combine like terms: 49 + -23 = 26 2r = 26 Divide each side by '2'. r = 13 Simplifying r = 13
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