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Simplifying -1(7 + 6r) + -5(1 + -4r) = 5r + 7r (7 * -1 + 6r * -1) + -5(1 + -4r) = 5r + 7r (-7 + -6r) + -5(1 + -4r) = 5r + 7r -7 + -6r + (1 * -5 + -4r * -5) = 5r + 7r -7 + -6r + (-5 + 20r) = 5r + 7r Reorder the terms: -7 + -5 + -6r + 20r = 5r + 7r Combine like terms: -7 + -5 = -12 -12 + -6r + 20r = 5r + 7r Combine like terms: -6r + 20r = 14r -12 + 14r = 5r + 7r Combine like terms: 5r + 7r = 12r -12 + 14r = 12r Solving -12 + 14r = 12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. -12 + 14r + -12r = 12r + -12r Combine like terms: 14r + -12r = 2r -12 + 2r = 12r + -12r Combine like terms: 12r + -12r = 0 -12 + 2r = 0 Add '12' to each side of the equation. -12 + 12 + 2r = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2r = 0 + 12 2r = 0 + 12 Combine like terms: 0 + 12 = 12 2r = 12 Divide each side by '2'. r = 6 Simplifying r = 6
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