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Simplifying 3(r + 7) = 2(5 + -1r) + 6 Reorder the terms: 3(7 + r) = 2(5 + -1r) + 6 (7 * 3 + r * 3) = 2(5 + -1r) + 6 (21 + 3r) = 2(5 + -1r) + 6 21 + 3r = (5 * 2 + -1r * 2) + 6 21 + 3r = (10 + -2r) + 6 Reorder the terms: 21 + 3r = 10 + 6 + -2r Combine like terms: 10 + 6 = 16 21 + 3r = 16 + -2r Solving 21 + 3r = 16 + -2r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2r' to each side of the equation. 21 + 3r + 2r = 16 + -2r + 2r Combine like terms: 3r + 2r = 5r 21 + 5r = 16 + -2r + 2r Combine like terms: -2r + 2r = 0 21 + 5r = 16 + 0 21 + 5r = 16 Add '-21' to each side of the equation. 21 + -21 + 5r = 16 + -21 Combine like terms: 21 + -21 = 0 0 + 5r = 16 + -21 5r = 16 + -21 Combine like terms: 16 + -21 = -5 5r = -5 Divide each side by '5'. r = -1 Simplifying r = -1
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