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Simplifying 6 + 2r + 4r + 1 = 6(r + -1) + -1(2r + 5) Reorder the terms: 6 + 1 + 2r + 4r = 6(r + -1) + -1(2r + 5) Combine like terms: 6 + 1 = 7 7 + 2r + 4r = 6(r + -1) + -1(2r + 5) Combine like terms: 2r + 4r = 6r 7 + 6r = 6(r + -1) + -1(2r + 5) Reorder the terms: 7 + 6r = 6(-1 + r) + -1(2r + 5) 7 + 6r = (-1 * 6 + r * 6) + -1(2r + 5) 7 + 6r = (-6 + 6r) + -1(2r + 5) Reorder the terms: 7 + 6r = -6 + 6r + -1(5 + 2r) 7 + 6r = -6 + 6r + (5 * -1 + 2r * -1) 7 + 6r = -6 + 6r + (-5 + -2r) Reorder the terms: 7 + 6r = -6 + -5 + 6r + -2r Combine like terms: -6 + -5 = -11 7 + 6r = -11 + 6r + -2r Combine like terms: 6r + -2r = 4r 7 + 6r = -11 + 4r Solving 7 + 6r = -11 + 4r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4r' to each side of the equation. 7 + 6r + -4r = -11 + 4r + -4r Combine like terms: 6r + -4r = 2r 7 + 2r = -11 + 4r + -4r Combine like terms: 4r + -4r = 0 7 + 2r = -11 + 0 7 + 2r = -11 Add '-7' to each side of the equation. 7 + -7 + 2r = -11 + -7 Combine like terms: 7 + -7 = 0 0 + 2r = -11 + -7 2r = -11 + -7 Combine like terms: -11 + -7 = -18 2r = -18 Divide each side by '2'. r = -9 Simplifying r = -9
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