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Simplifying 5(r + -6) = 3[2 + -1(5 + -1r)] Reorder the terms: 5(-6 + r) = 3[2 + -1(5 + -1r)] (-6 * 5 + r * 5) = 3[2 + -1(5 + -1r)] (-30 + 5r) = 3[2 + -1(5 + -1r)] -30 + 5r = 3[2 + (5 * -1 + -1r * -1)] -30 + 5r = 3[2 + (-5 + 1r)] Combine like terms: 2 + -5 = -3 -30 + 5r = 3[-3 + 1r] -30 + 5r = [-3 * 3 + 1r * 3] -30 + 5r = [-9 + 3r] Solving -30 + 5r = -9 + 3r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3r' to each side of the equation. -30 + 5r + -3r = -9 + 3r + -3r Combine like terms: 5r + -3r = 2r -30 + 2r = -9 + 3r + -3r Combine like terms: 3r + -3r = 0 -30 + 2r = -9 + 0 -30 + 2r = -9 Add '30' to each side of the equation. -30 + 30 + 2r = -9 + 30 Combine like terms: -30 + 30 = 0 0 + 2r = -9 + 30 2r = -9 + 30 Combine like terms: -9 + 30 = 21 2r = 21 Divide each side by '2'. r = 10.5 Simplifying r = 10.5
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