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Simplifying 6(r + -5) + -5(r + -1) = 2(r + 3) Reorder the terms: 6(-5 + r) + -5(r + -1) = 2(r + 3) (-5 * 6 + r * 6) + -5(r + -1) = 2(r + 3) (-30 + 6r) + -5(r + -1) = 2(r + 3) Reorder the terms: -30 + 6r + -5(-1 + r) = 2(r + 3) -30 + 6r + (-1 * -5 + r * -5) = 2(r + 3) -30 + 6r + (5 + -5r) = 2(r + 3) Reorder the terms: -30 + 5 + 6r + -5r = 2(r + 3) Combine like terms: -30 + 5 = -25 -25 + 6r + -5r = 2(r + 3) Combine like terms: 6r + -5r = 1r -25 + 1r = 2(r + 3) Reorder the terms: -25 + 1r = 2(3 + r) -25 + 1r = (3 * 2 + r * 2) -25 + 1r = (6 + 2r) Solving -25 + 1r = 6 + 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. -25 + 1r + -2r = 6 + 2r + -2r Combine like terms: 1r + -2r = -1r -25 + -1r = 6 + 2r + -2r Combine like terms: 2r + -2r = 0 -25 + -1r = 6 + 0 -25 + -1r = 6 Add '25' to each side of the equation. -25 + 25 + -1r = 6 + 25 Combine like terms: -25 + 25 = 0 0 + -1r = 6 + 25 -1r = 6 + 25 Combine like terms: 6 + 25 = 31 -1r = 31 Divide each side by '-1'. r = -31 Simplifying r = -31
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