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Simplifying 54 = 2(v + 5) + 1(3v + -1) Reorder the terms: 54 = 2(5 + v) + 1(3v + -1) 54 = (5 * 2 + v * 2) + 1(3v + -1) 54 = (10 + 2v) + 1(3v + -1) Reorder the terms: 54 = 10 + 2v + 1(-1 + 3v) 54 = 10 + 2v + (-1 * 1 + 3v * 1) 54 = 10 + 2v + (-1 + 3v) Reorder the terms: 54 = 10 + -1 + 2v + 3v Combine like terms: 10 + -1 = 9 54 = 9 + 2v + 3v Combine like terms: 2v + 3v = 5v 54 = 9 + 5v Solving 54 = 9 + 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. 54 + -5v = 9 + 5v + -5v Combine like terms: 5v + -5v = 0 54 + -5v = 9 + 0 54 + -5v = 9 Add '-54' to each side of the equation. 54 + -54 + -5v = 9 + -54 Combine like terms: 54 + -54 = 0 0 + -5v = 9 + -54 -5v = 9 + -54 Combine like terms: 9 + -54 = -45 -5v = -45 Divide each side by '-5'. v = 9 Simplifying v = 9
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