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Simplifying 3(5 + 7r) + -3(10r + -10) = -5 + -10r + 2r (5 * 3 + 7r * 3) + -3(10r + -10) = -5 + -10r + 2r (15 + 21r) + -3(10r + -10) = -5 + -10r + 2r Reorder the terms: 15 + 21r + -3(-10 + 10r) = -5 + -10r + 2r 15 + 21r + (-10 * -3 + 10r * -3) = -5 + -10r + 2r 15 + 21r + (30 + -30r) = -5 + -10r + 2r Reorder the terms: 15 + 30 + 21r + -30r = -5 + -10r + 2r Combine like terms: 15 + 30 = 45 45 + 21r + -30r = -5 + -10r + 2r Combine like terms: 21r + -30r = -9r 45 + -9r = -5 + -10r + 2r Combine like terms: -10r + 2r = -8r 45 + -9r = -5 + -8r Solving 45 + -9r = -5 + -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. 45 + -9r + 8r = -5 + -8r + 8r Combine like terms: -9r + 8r = -1r 45 + -1r = -5 + -8r + 8r Combine like terms: -8r + 8r = 0 45 + -1r = -5 + 0 45 + -1r = -5 Add '-45' to each side of the equation. 45 + -45 + -1r = -5 + -45 Combine like terms: 45 + -45 = 0 0 + -1r = -5 + -45 -1r = -5 + -45 Combine like terms: -5 + -45 = -50 -1r = -50 Divide each side by '-1'. r = 50 Simplifying r = 50
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