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Simplifying 2(2r + -9) + -7(r + 6) = 1 + -9r + -4r + 9 Reorder the terms: 2(-9 + 2r) + -7(r + 6) = 1 + -9r + -4r + 9 (-9 * 2 + 2r * 2) + -7(r + 6) = 1 + -9r + -4r + 9 (-18 + 4r) + -7(r + 6) = 1 + -9r + -4r + 9 Reorder the terms: -18 + 4r + -7(6 + r) = 1 + -9r + -4r + 9 -18 + 4r + (6 * -7 + r * -7) = 1 + -9r + -4r + 9 -18 + 4r + (-42 + -7r) = 1 + -9r + -4r + 9 Reorder the terms: -18 + -42 + 4r + -7r = 1 + -9r + -4r + 9 Combine like terms: -18 + -42 = -60 -60 + 4r + -7r = 1 + -9r + -4r + 9 Combine like terms: 4r + -7r = -3r -60 + -3r = 1 + -9r + -4r + 9 Reorder the terms: -60 + -3r = 1 + 9 + -9r + -4r Combine like terms: 1 + 9 = 10 -60 + -3r = 10 + -9r + -4r Combine like terms: -9r + -4r = -13r -60 + -3r = 10 + -13r Solving -60 + -3r = 10 + -13r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '13r' to each side of the equation. -60 + -3r + 13r = 10 + -13r + 13r Combine like terms: -3r + 13r = 10r -60 + 10r = 10 + -13r + 13r Combine like terms: -13r + 13r = 0 -60 + 10r = 10 + 0 -60 + 10r = 10 Add '60' to each side of the equation. -60 + 60 + 10r = 10 + 60 Combine like terms: -60 + 60 = 0 0 + 10r = 10 + 60 10r = 10 + 60 Combine like terms: 10 + 60 = 70 10r = 70 Divide each side by '10'. r = 7 Simplifying r = 7
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