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Simplifying 8(r + -3) + -7(r + -1) = 2(r + 7) Reorder the terms: 8(-3 + r) + -7(r + -1) = 2(r + 7) (-3 * 8 + r * 8) + -7(r + -1) = 2(r + 7) (-24 + 8r) + -7(r + -1) = 2(r + 7) Reorder the terms: -24 + 8r + -7(-1 + r) = 2(r + 7) -24 + 8r + (-1 * -7 + r * -7) = 2(r + 7) -24 + 8r + (7 + -7r) = 2(r + 7) Reorder the terms: -24 + 7 + 8r + -7r = 2(r + 7) Combine like terms: -24 + 7 = -17 -17 + 8r + -7r = 2(r + 7) Combine like terms: 8r + -7r = 1r -17 + 1r = 2(r + 7) Reorder the terms: -17 + 1r = 2(7 + r) -17 + 1r = (7 * 2 + r * 2) -17 + 1r = (14 + 2r) Solving -17 + 1r = 14 + 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. -17 + 1r + -2r = 14 + 2r + -2r Combine like terms: 1r + -2r = -1r -17 + -1r = 14 + 2r + -2r Combine like terms: 2r + -2r = 0 -17 + -1r = 14 + 0 -17 + -1r = 14 Add '17' to each side of the equation. -17 + 17 + -1r = 14 + 17 Combine like terms: -17 + 17 = 0 0 + -1r = 14 + 17 -1r = 14 + 17 Combine like terms: 14 + 17 = 31 -1r = 31 Divide each side by '-1'. r = -31 Simplifying r = -31
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