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Simplifying 51 = -6(r + 4) + -7(1 + 5r) Reorder the terms: 51 = -6(4 + r) + -7(1 + 5r) 51 = (4 * -6 + r * -6) + -7(1 + 5r) 51 = (-24 + -6r) + -7(1 + 5r) 51 = -24 + -6r + (1 * -7 + 5r * -7) 51 = -24 + -6r + (-7 + -35r) Reorder the terms: 51 = -24 + -7 + -6r + -35r Combine like terms: -24 + -7 = -31 51 = -31 + -6r + -35r Combine like terms: -6r + -35r = -41r 51 = -31 + -41r Solving 51 = -31 + -41r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '41r' to each side of the equation. 51 + 41r = -31 + -41r + 41r Combine like terms: -41r + 41r = 0 51 + 41r = -31 + 0 51 + 41r = -31 Add '-51' to each side of the equation. 51 + -51 + 41r = -31 + -51 Combine like terms: 51 + -51 = 0 0 + 41r = -31 + -51 41r = -31 + -51 Combine like terms: -31 + -51 = -82 41r = -82 Divide each side by '41'. r = -2 Simplifying r = -2
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