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Simplifying 7v + 5v = 4(1 + 6v) + 8(1 + -2v) Combine like terms: 7v + 5v = 12v 12v = 4(1 + 6v) + 8(1 + -2v) 12v = (1 * 4 + 6v * 4) + 8(1 + -2v) 12v = (4 + 24v) + 8(1 + -2v) 12v = 4 + 24v + (1 * 8 + -2v * 8) 12v = 4 + 24v + (8 + -16v) Reorder the terms: 12v = 4 + 8 + 24v + -16v Combine like terms: 4 + 8 = 12 12v = 12 + 24v + -16v Combine like terms: 24v + -16v = 8v 12v = 12 + 8v Solving 12v = 12 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. 12v + -8v = 12 + 8v + -8v Combine like terms: 12v + -8v = 4v 4v = 12 + 8v + -8v Combine like terms: 8v + -8v = 0 4v = 12 + 0 4v = 12 Divide each side by '4'. v = 3 Simplifying v = 3
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