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Simplifying -7(5r + 1) + 5r = -6 + 6(-4r + 3) Reorder the terms: -7(1 + 5r) + 5r = -6 + 6(-4r + 3) (1 * -7 + 5r * -7) + 5r = -6 + 6(-4r + 3) (-7 + -35r) + 5r = -6 + 6(-4r + 3) Combine like terms: -35r + 5r = -30r -7 + -30r = -6 + 6(-4r + 3) Reorder the terms: -7 + -30r = -6 + 6(3 + -4r) -7 + -30r = -6 + (3 * 6 + -4r * 6) -7 + -30r = -6 + (18 + -24r) Combine like terms: -6 + 18 = 12 -7 + -30r = 12 + -24r Solving -7 + -30r = 12 + -24r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '24r' to each side of the equation. -7 + -30r + 24r = 12 + -24r + 24r Combine like terms: -30r + 24r = -6r -7 + -6r = 12 + -24r + 24r Combine like terms: -24r + 24r = 0 -7 + -6r = 12 + 0 -7 + -6r = 12 Add '7' to each side of the equation. -7 + 7 + -6r = 12 + 7 Combine like terms: -7 + 7 = 0 0 + -6r = 12 + 7 -6r = 12 + 7 Combine like terms: 12 + 7 = 19 -6r = 19 Divide each side by '-6'. r = -3.166666667 Simplifying r = -3.166666667
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