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Simplifying 3(r + -1) = 5(r + -3) + 8 Reorder the terms: 3(-1 + r) = 5(r + -3) + 8 (-1 * 3 + r * 3) = 5(r + -3) + 8 (-3 + 3r) = 5(r + -3) + 8 Reorder the terms: -3 + 3r = 5(-3 + r) + 8 -3 + 3r = (-3 * 5 + r * 5) + 8 -3 + 3r = (-15 + 5r) + 8 Reorder the terms: -3 + 3r = -15 + 8 + 5r Combine like terms: -15 + 8 = -7 -3 + 3r = -7 + 5r Solving -3 + 3r = -7 + 5r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5r' to each side of the equation. -3 + 3r + -5r = -7 + 5r + -5r Combine like terms: 3r + -5r = -2r -3 + -2r = -7 + 5r + -5r Combine like terms: 5r + -5r = 0 -3 + -2r = -7 + 0 -3 + -2r = -7 Add '3' to each side of the equation. -3 + 3 + -2r = -7 + 3 Combine like terms: -3 + 3 = 0 0 + -2r = -7 + 3 -2r = -7 + 3 Combine like terms: -7 + 3 = -4 -2r = -4 Divide each side by '-2'. r = 2 Simplifying r = 2
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