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Simplifying 6(r + -2) + -5(r + -1) = 2(r + 3) Reorder the terms: 6(-2 + r) + -5(r + -1) = 2(r + 3) (-2 * 6 + r * 6) + -5(r + -1) = 2(r + 3) (-12 + 6r) + -5(r + -1) = 2(r + 3) Reorder the terms: -12 + 6r + -5(-1 + r) = 2(r + 3) -12 + 6r + (-1 * -5 + r * -5) = 2(r + 3) -12 + 6r + (5 + -5r) = 2(r + 3) Reorder the terms: -12 + 5 + 6r + -5r = 2(r + 3) Combine like terms: -12 + 5 = -7 -7 + 6r + -5r = 2(r + 3) Combine like terms: 6r + -5r = 1r -7 + 1r = 2(r + 3) Reorder the terms: -7 + 1r = 2(3 + r) -7 + 1r = (3 * 2 + r * 2) -7 + 1r = (6 + 2r) Solving -7 + 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. -7 + 1r + -2r = 6 + 2r + -2r Combine like terms: 1r + -2r = -1r -7 + -1r = 6 + 2r + -2r Combine like terms: 2r + -2r = 0 -7 + -1r = 6 + 0 -7 + -1r = 6 Add '7' to each side of the equation. -7 + 7 + -1r = 6 + 7 Combine like terms: -7 + 7 = 0 0 + -1r = 6 + 7 -1r = 6 + 7 Combine like terms: 6 + 7 = 13 -1r = 13 Divide each side by '-1'. r = -13 Simplifying r = -13
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