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Simplifying 5(3r + -1) + -1(r + -1) = 1 + 5 + 3r + -5 Reorder the terms: 5(-1 + 3r) + -1(r + -1) = 1 + 5 + 3r + -5 (-1 * 5 + 3r * 5) + -1(r + -1) = 1 + 5 + 3r + -5 (-5 + 15r) + -1(r + -1) = 1 + 5 + 3r + -5 Reorder the terms: -5 + 15r + -1(-1 + r) = 1 + 5 + 3r + -5 -5 + 15r + (-1 * -1 + r * -1) = 1 + 5 + 3r + -5 -5 + 15r + (1 + -1r) = 1 + 5 + 3r + -5 Reorder the terms: -5 + 1 + 15r + -1r = 1 + 5 + 3r + -5 Combine like terms: -5 + 1 = -4 -4 + 15r + -1r = 1 + 5 + 3r + -5 Combine like terms: 15r + -1r = 14r -4 + 14r = 1 + 5 + 3r + -5 Reorder the terms: -4 + 14r = 1 + 5 + -5 + 3r Combine like terms: 1 + 5 = 6 -4 + 14r = 6 + -5 + 3r Combine like terms: 6 + -5 = 1 -4 + 14r = 1 + 3r Solving -4 + 14r = 1 + 3r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3r' to each side of the equation. -4 + 14r + -3r = 1 + 3r + -3r Combine like terms: 14r + -3r = 11r -4 + 11r = 1 + 3r + -3r Combine like terms: 3r + -3r = 0 -4 + 11r = 1 + 0 -4 + 11r = 1 Add '4' to each side of the equation. -4 + 4 + 11r = 1 + 4 Combine like terms: -4 + 4 = 0 0 + 11r = 1 + 4 11r = 1 + 4 Combine like terms: 1 + 4 = 5 11r = 5 Divide each side by '11'. r = 0.4545454545 Simplifying r = 0.4545454545
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