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Simplifying 2(1 + 4r) + -3(7 + -3r) = -8r + 6r (1 * 2 + 4r * 2) + -3(7 + -3r) = -8r + 6r (2 + 8r) + -3(7 + -3r) = -8r + 6r 2 + 8r + (7 * -3 + -3r * -3) = -8r + 6r 2 + 8r + (-21 + 9r) = -8r + 6r Reorder the terms: 2 + -21 + 8r + 9r = -8r + 6r Combine like terms: 2 + -21 = -19 -19 + 8r + 9r = -8r + 6r Combine like terms: 8r + 9r = 17r -19 + 17r = -8r + 6r Combine like terms: -8r + 6r = -2r -19 + 17r = -2r Solving -19 + 17r = -2r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2r' to each side of the equation. -19 + 17r + 2r = -2r + 2r Combine like terms: 17r + 2r = 19r -19 + 19r = -2r + 2r Combine like terms: -2r + 2r = 0 -19 + 19r = 0 Add '19' to each side of the equation. -19 + 19 + 19r = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 19r = 0 + 19 19r = 0 + 19 Combine like terms: 0 + 19 = 19 19r = 19 Divide each side by '19'. r = 1 Simplifying r = 1
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