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Simplifying 5(r + -1) + -6 = 7 + -1(r + 5) Reorder the terms: 5(-1 + r) + -6 = 7 + -1(r + 5) (-1 * 5 + r * 5) + -6 = 7 + -1(r + 5) (-5 + 5r) + -6 = 7 + -1(r + 5) Reorder the terms: -5 + -6 + 5r = 7 + -1(r + 5) Combine like terms: -5 + -6 = -11 -11 + 5r = 7 + -1(r + 5) Reorder the terms: -11 + 5r = 7 + -1(5 + r) -11 + 5r = 7 + (5 * -1 + r * -1) -11 + 5r = 7 + (-5 + -1r) Combine like terms: 7 + -5 = 2 -11 + 5r = 2 + -1r Solving -11 + 5r = 2 + -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. -11 + 5r + r = 2 + -1r + r Combine like terms: 5r + r = 6r -11 + 6r = 2 + -1r + r Combine like terms: -1r + r = 0 -11 + 6r = 2 + 0 -11 + 6r = 2 Add '11' to each side of the equation. -11 + 11 + 6r = 2 + 11 Combine like terms: -11 + 11 = 0 0 + 6r = 2 + 11 6r = 2 + 11 Combine like terms: 2 + 11 = 13 6r = 13 Divide each side by '6'. r = 2.166666667 Simplifying r = 2.166666667
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