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Simplifying 3(1 + 3v) + 3v = 5(v + 1) + 5 (1 * 3 + 3v * 3) + 3v = 5(v + 1) + 5 (3 + 9v) + 3v = 5(v + 1) + 5 Combine like terms: 9v + 3v = 12v 3 + 12v = 5(v + 1) + 5 Reorder the terms: 3 + 12v = 5(1 + v) + 5 3 + 12v = (1 * 5 + v * 5) + 5 3 + 12v = (5 + 5v) + 5 Reorder the terms: 3 + 12v = 5 + 5 + 5v Combine like terms: 5 + 5 = 10 3 + 12v = 10 + 5v Solving 3 + 12v = 10 + 5v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5v' to each side of the equation. 3 + 12v + -5v = 10 + 5v + -5v Combine like terms: 12v + -5v = 7v 3 + 7v = 10 + 5v + -5v Combine like terms: 5v + -5v = 0 3 + 7v = 10 + 0 3 + 7v = 10 Add '-3' to each side of the equation. 3 + -3 + 7v = 10 + -3 Combine like terms: 3 + -3 = 0 0 + 7v = 10 + -3 7v = 10 + -3 Combine like terms: 10 + -3 = 7 7v = 7 Divide each side by '7'. v = 1 Simplifying v = 1
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