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Simplifying 9 + 5(r + 3) = 6 + 3(r + -2) Reorder the terms: 9 + 5(3 + r) = 6 + 3(r + -2) 9 + (3 * 5 + r * 5) = 6 + 3(r + -2) 9 + (15 + 5r) = 6 + 3(r + -2) Combine like terms: 9 + 15 = 24 24 + 5r = 6 + 3(r + -2) Reorder the terms: 24 + 5r = 6 + 3(-2 + r) 24 + 5r = 6 + (-2 * 3 + r * 3) 24 + 5r = 6 + (-6 + 3r) Combine like terms: 6 + -6 = 0 24 + 5r = 0 + 3r 24 + 5r = 3r Solving 24 + 5r = 3r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3r' to each side of the equation. 24 + 5r + -3r = 3r + -3r Combine like terms: 5r + -3r = 2r 24 + 2r = 3r + -3r Combine like terms: 3r + -3r = 0 24 + 2r = 0 Add '-24' to each side of the equation. 24 + -24 + 2r = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 2r = 0 + -24 2r = 0 + -24 Combine like terms: 0 + -24 = -24 2r = -24 Divide each side by '2'. r = -12 Simplifying r = -12
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