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Simplifying 3(r + 2) + -5(4 + -1r) + 2 = 12 Reorder the terms: 3(2 + r) + -5(4 + -1r) + 2 = 12 (2 * 3 + r * 3) + -5(4 + -1r) + 2 = 12 (6 + 3r) + -5(4 + -1r) + 2 = 12 6 + 3r + (4 * -5 + -1r * -5) + 2 = 12 6 + 3r + (-20 + 5r) + 2 = 12 Reorder the terms: 6 + -20 + 2 + 3r + 5r = 12 Combine like terms: 6 + -20 = -14 -14 + 2 + 3r + 5r = 12 Combine like terms: -14 + 2 = -12 -12 + 3r + 5r = 12 Combine like terms: 3r + 5r = 8r -12 + 8r = 12 Solving -12 + 8r = 12 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + 8r = 12 + 12 Combine like terms: -12 + 12 = 0 0 + 8r = 12 + 12 8r = 12 + 12 Combine like terms: 12 + 12 = 24 8r = 24 Divide each side by '8'. r = 3 Simplifying r = 3
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