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Simplifying 6(r + -6) + -5(r + -1) = 2(r + 5) Reorder the terms: 6(-6 + r) + -5(r + -1) = 2(r + 5) (-6 * 6 + r * 6) + -5(r + -1) = 2(r + 5) (-36 + 6r) + -5(r + -1) = 2(r + 5) Reorder the terms: -36 + 6r + -5(-1 + r) = 2(r + 5) -36 + 6r + (-1 * -5 + r * -5) = 2(r + 5) -36 + 6r + (5 + -5r) = 2(r + 5) Reorder the terms: -36 + 5 + 6r + -5r = 2(r + 5) Combine like terms: -36 + 5 = -31 -31 + 6r + -5r = 2(r + 5) Combine like terms: 6r + -5r = 1r -31 + 1r = 2(r + 5) Reorder the terms: -31 + 1r = 2(5 + r) -31 + 1r = (5 * 2 + r * 2) -31 + 1r = (10 + 2r) Solving -31 + 1r = 10 + 2r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2r' to each side of the equation. -31 + 1r + -2r = 10 + 2r + -2r Combine like terms: 1r + -2r = -1r -31 + -1r = 10 + 2r + -2r Combine like terms: 2r + -2r = 0 -31 + -1r = 10 + 0 -31 + -1r = 10 Add '31' to each side of the equation. -31 + 31 + -1r = 10 + 31 Combine like terms: -31 + 31 = 0 0 + -1r = 10 + 31 -1r = 10 + 31 Combine like terms: 10 + 31 = 41 -1r = 41 Divide each side by '-1'. r = -41 Simplifying r = -41
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