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Simplifying 5(6r + 4) + 5(-3r + 2) = 7r + 4 + r + -2 Reorder the terms: 5(4 + 6r) + 5(-3r + 2) = 7r + 4 + r + -2 (4 * 5 + 6r * 5) + 5(-3r + 2) = 7r + 4 + r + -2 (20 + 30r) + 5(-3r + 2) = 7r + 4 + r + -2 Reorder the terms: 20 + 30r + 5(2 + -3r) = 7r + 4 + r + -2 20 + 30r + (2 * 5 + -3r * 5) = 7r + 4 + r + -2 20 + 30r + (10 + -15r) = 7r + 4 + r + -2 Reorder the terms: 20 + 10 + 30r + -15r = 7r + 4 + r + -2 Combine like terms: 20 + 10 = 30 30 + 30r + -15r = 7r + 4 + r + -2 Combine like terms: 30r + -15r = 15r 30 + 15r = 7r + 4 + r + -2 Reorder the terms: 30 + 15r = 4 + -2 + 7r + r Combine like terms: 4 + -2 = 2 30 + 15r = 2 + 7r + r Combine like terms: 7r + r = 8r 30 + 15r = 2 + 8r Solving 30 + 15r = 2 + 8r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8r' to each side of the equation. 30 + 15r + -8r = 2 + 8r + -8r Combine like terms: 15r + -8r = 7r 30 + 7r = 2 + 8r + -8r Combine like terms: 8r + -8r = 0 30 + 7r = 2 + 0 30 + 7r = 2 Add '-30' to each side of the equation. 30 + -30 + 7r = 2 + -30 Combine like terms: 30 + -30 = 0 0 + 7r = 2 + -30 7r = 2 + -30 Combine like terms: 2 + -30 = -28 7r = -28 Divide each side by '7'. r = -4 Simplifying r = -4
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