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Simplifying 5(r + -6) = 6(r + 7) + -9r Reorder the terms: 5(-6 + r) = 6(r + 7) + -9r (-6 * 5 + r * 5) = 6(r + 7) + -9r (-30 + 5r) = 6(r + 7) + -9r Reorder the terms: -30 + 5r = 6(7 + r) + -9r -30 + 5r = (7 * 6 + r * 6) + -9r -30 + 5r = (42 + 6r) + -9r Combine like terms: 6r + -9r = -3r -30 + 5r = 42 + -3r Solving -30 + 5r = 42 + -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. -30 + 5r + 3r = 42 + -3r + 3r Combine like terms: 5r + 3r = 8r -30 + 8r = 42 + -3r + 3r Combine like terms: -3r + 3r = 0 -30 + 8r = 42 + 0 -30 + 8r = 42 Add '30' to each side of the equation. -30 + 30 + 8r = 42 + 30 Combine like terms: -30 + 30 = 0 0 + 8r = 42 + 30 8r = 42 + 30 Combine like terms: 42 + 30 = 72 8r = 72 Divide each side by '8'. r = 9 Simplifying r = 9
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