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Simplifying 6(1 + -6r) + 5(-7 + -1r) = -8r + -4r (1 * 6 + -6r * 6) + 5(-7 + -1r) = -8r + -4r (6 + -36r) + 5(-7 + -1r) = -8r + -4r 6 + -36r + (-7 * 5 + -1r * 5) = -8r + -4r 6 + -36r + (-35 + -5r) = -8r + -4r Reorder the terms: 6 + -35 + -36r + -5r = -8r + -4r Combine like terms: 6 + -35 = -29 -29 + -36r + -5r = -8r + -4r Combine like terms: -36r + -5r = -41r -29 + -41r = -8r + -4r Combine like terms: -8r + -4r = -12r -29 + -41r = -12r Solving -29 + -41r = -12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12r' to each side of the equation. -29 + -41r + 12r = -12r + 12r Combine like terms: -41r + 12r = -29r -29 + -29r = -12r + 12r Combine like terms: -12r + 12r = 0 -29 + -29r = 0 Add '29' to each side of the equation. -29 + 29 + -29r = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -29r = 0 + 29 -29r = 0 + 29 Combine like terms: 0 + 29 = 29 -29r = 29 Divide each side by '-29'. r = -1 Simplifying r = -1
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