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Simplifying 9 + -5(3r + 20) + 2r = 17r + 109 Reorder the terms: 9 + -5(20 + 3r) + 2r = 17r + 109 9 + (20 * -5 + 3r * -5) + 2r = 17r + 109 9 + (-100 + -15r) + 2r = 17r + 109 Combine like terms: 9 + -100 = -91 -91 + -15r + 2r = 17r + 109 Combine like terms: -15r + 2r = -13r -91 + -13r = 17r + 109 Reorder the terms: -91 + -13r = 109 + 17r Solving -91 + -13r = 109 + 17r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-17r' to each side of the equation. -91 + -13r + -17r = 109 + 17r + -17r Combine like terms: -13r + -17r = -30r -91 + -30r = 109 + 17r + -17r Combine like terms: 17r + -17r = 0 -91 + -30r = 109 + 0 -91 + -30r = 109 Add '91' to each side of the equation. -91 + 91 + -30r = 109 + 91 Combine like terms: -91 + 91 = 0 0 + -30r = 109 + 91 -30r = 109 + 91 Combine like terms: 109 + 91 = 200 -30r = 200 Divide each side by '-30'. r = -6.666666667 Simplifying r = -6.666666667
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