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Simplifying 5(6 + 5r) + -2(r + 3) = 8r + -3 + 6r (6 * 5 + 5r * 5) + -2(r + 3) = 8r + -3 + 6r (30 + 25r) + -2(r + 3) = 8r + -3 + 6r Reorder the terms: 30 + 25r + -2(3 + r) = 8r + -3 + 6r 30 + 25r + (3 * -2 + r * -2) = 8r + -3 + 6r 30 + 25r + (-6 + -2r) = 8r + -3 + 6r Reorder the terms: 30 + -6 + 25r + -2r = 8r + -3 + 6r Combine like terms: 30 + -6 = 24 24 + 25r + -2r = 8r + -3 + 6r Combine like terms: 25r + -2r = 23r 24 + 23r = 8r + -3 + 6r Reorder the terms: 24 + 23r = -3 + 8r + 6r Combine like terms: 8r + 6r = 14r 24 + 23r = -3 + 14r Solving 24 + 23r = -3 + 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. 24 + 23r + -14r = -3 + 14r + -14r Combine like terms: 23r + -14r = 9r 24 + 9r = -3 + 14r + -14r Combine like terms: 14r + -14r = 0 24 + 9r = -3 + 0 24 + 9r = -3 Add '-24' to each side of the equation. 24 + -24 + 9r = -3 + -24 Combine like terms: 24 + -24 = 0 0 + 9r = -3 + -24 9r = -3 + -24 Combine like terms: -3 + -24 = -27 9r = -27 Divide each side by '9'. r = -3 Simplifying r = -3
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