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Simplifying 6 + -5(2 + -3r) + 7 = 4(r + -6) + -17 6 + (2 * -5 + -3r * -5) + 7 = 4(r + -6) + -17 6 + (-10 + 15r) + 7 = 4(r + -6) + -17 Reorder the terms: 6 + -10 + 7 + 15r = 4(r + -6) + -17 Combine like terms: 6 + -10 = -4 -4 + 7 + 15r = 4(r + -6) + -17 Combine like terms: -4 + 7 = 3 3 + 15r = 4(r + -6) + -17 Reorder the terms: 3 + 15r = 4(-6 + r) + -17 3 + 15r = (-6 * 4 + r * 4) + -17 3 + 15r = (-24 + 4r) + -17 Reorder the terms: 3 + 15r = -24 + -17 + 4r Combine like terms: -24 + -17 = -41 3 + 15r = -41 + 4r Solving 3 + 15r = -41 + 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. 3 + 15r + -4r = -41 + 4r + -4r Combine like terms: 15r + -4r = 11r 3 + 11r = -41 + 4r + -4r Combine like terms: 4r + -4r = 0 3 + 11r = -41 + 0 3 + 11r = -41 Add '-3' to each side of the equation. 3 + -3 + 11r = -41 + -3 Combine like terms: 3 + -3 = 0 0 + 11r = -41 + -3 11r = -41 + -3 Combine like terms: -41 + -3 = -44 11r = -44 Divide each side by '11'. r = -4 Simplifying r = -4
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