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Simplifying -5v + 12v = 6(12 + -11v) + -7(12 + -11v) Combine like terms: -5v + 12v = 7v 7v = 6(12 + -11v) + -7(12 + -11v) 7v = (12 * 6 + -11v * 6) + -7(12 + -11v) 7v = (72 + -66v) + -7(12 + -11v) 7v = 72 + -66v + (12 * -7 + -11v * -7) 7v = 72 + -66v + (-84 + 77v) Reorder the terms: 7v = 72 + -84 + -66v + 77v Combine like terms: 72 + -84 = -12 7v = -12 + -66v + 77v Combine like terms: -66v + 77v = 11v 7v = -12 + 11v Solving 7v = -12 + 11v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-11v' to each side of the equation. 7v + -11v = -12 + 11v + -11v Combine like terms: 7v + -11v = -4v -4v = -12 + 11v + -11v Combine like terms: 11v + -11v = 0 -4v = -12 + 0 -4v = -12 Divide each side by '-4'. v = 3 Simplifying v = 3
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