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Simplifying 3r + 7(1 + 6r) = -34 + 4r 3r + (1 * 7 + 6r * 7) = -34 + 4r 3r + (7 + 42r) = -34 + 4r Reorder the terms: 7 + 3r + 42r = -34 + 4r Combine like terms: 3r + 42r = 45r 7 + 45r = -34 + 4r Solving 7 + 45r = -34 + 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 + 45r + -4r = -34 + 4r + -4r Combine like terms: 45r + -4r = 41r 7 + 41r = -34 + 4r + -4r Combine like terms: 4r + -4r = 0 7 + 41r = -34 + 0 7 + 41r = -34 Add '-7' to each side of the equation. 7 + -7 + 41r = -34 + -7 Combine like terms: 7 + -7 = 0 0 + 41r = -34 + -7 41r = -34 + -7 Combine like terms: -34 + -7 = -41 41r = -41 Divide each side by '41'. r = -1 Simplifying r = -1
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