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Simplifying 6(r + -4) + -5(r + -1) = 2(r + 6) Reorder the terms: 6(-4 + r) + -5(r + -1) = 2(r + 6) (-4 * 6 + r * 6) + -5(r + -1) = 2(r + 6) (-24 + 6r) + -5(r + -1) = 2(r + 6) Reorder the terms: -24 + 6r + -5(-1 + r) = 2(r + 6) -24 + 6r + (-1 * -5 + r * -5) = 2(r + 6) -24 + 6r + (5 + -5r) = 2(r + 6) Reorder the terms: -24 + 5 + 6r + -5r = 2(r + 6) Combine like terms: -24 + 5 = -19 -19 + 6r + -5r = 2(r + 6) Combine like terms: 6r + -5r = 1r -19 + 1r = 2(r + 6) Reorder the terms: -19 + 1r = 2(6 + r) -19 + 1r = (6 * 2 + r * 2) -19 + 1r = (12 + 2r) Solving -19 + 1r = 12 + 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. -19 + 1r + -2r = 12 + 2r + -2r Combine like terms: 1r + -2r = -1r -19 + -1r = 12 + 2r + -2r Combine like terms: 2r + -2r = 0 -19 + -1r = 12 + 0 -19 + -1r = 12 Add '19' to each side of the equation. -19 + 19 + -1r = 12 + 19 Combine like terms: -19 + 19 = 0 0 + -1r = 12 + 19 -1r = 12 + 19 Combine like terms: 12 + 19 = 31 -1r = 31 Divide each side by '-1'. r = -31 Simplifying r = -31
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