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Simplifying -5(1 + -6r) = 7(11r + 6) (1 * -5 + -6r * -5) = 7(11r + 6) (-5 + 30r) = 7(11r + 6) Reorder the terms: -5 + 30r = 7(6 + 11r) -5 + 30r = (6 * 7 + 11r * 7) -5 + 30r = (42 + 77r) Solving -5 + 30r = 42 + 77r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-77r' to each side of the equation. -5 + 30r + -77r = 42 + 77r + -77r Combine like terms: 30r + -77r = -47r -5 + -47r = 42 + 77r + -77r Combine like terms: 77r + -77r = 0 -5 + -47r = 42 + 0 -5 + -47r = 42 Add '5' to each side of the equation. -5 + 5 + -47r = 42 + 5 Combine like terms: -5 + 5 = 0 0 + -47r = 42 + 5 -47r = 42 + 5 Combine like terms: 42 + 5 = 47 -47r = 47 Divide each side by '-47'. r = -1 Simplifying r = -1
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