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Simplifying -7(8 + -1r) + -2(9r + 12) = -7r + 6r (8 * -7 + -1r * -7) + -2(9r + 12) = -7r + 6r (-56 + 7r) + -2(9r + 12) = -7r + 6r Reorder the terms: -56 + 7r + -2(12 + 9r) = -7r + 6r -56 + 7r + (12 * -2 + 9r * -2) = -7r + 6r -56 + 7r + (-24 + -18r) = -7r + 6r Reorder the terms: -56 + -24 + 7r + -18r = -7r + 6r Combine like terms: -56 + -24 = -80 -80 + 7r + -18r = -7r + 6r Combine like terms: 7r + -18r = -11r -80 + -11r = -7r + 6r Combine like terms: -7r + 6r = -1r -80 + -11r = -1r Solving -80 + -11r = -1r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add 'r' to each side of the equation. -80 + -11r + r = -1r + r Combine like terms: -11r + r = -10r -80 + -10r = -1r + r Combine like terms: -1r + r = 0 -80 + -10r = 0 Add '80' to each side of the equation. -80 + 80 + -10r = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -10r = 0 + 80 -10r = 0 + 80 Combine like terms: 0 + 80 = 80 -10r = 80 Divide each side by '-10'. r = -8 Simplifying r = -8
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