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Simplifying 43 = 2(3 + 7v) + -1(7 + -8v) 43 = (3 * 2 + 7v * 2) + -1(7 + -8v) 43 = (6 + 14v) + -1(7 + -8v) 43 = 6 + 14v + (7 * -1 + -8v * -1) 43 = 6 + 14v + (-7 + 8v) Reorder the terms: 43 = 6 + -7 + 14v + 8v Combine like terms: 6 + -7 = -1 43 = -1 + 14v + 8v Combine like terms: 14v + 8v = 22v 43 = -1 + 22v Solving 43 = -1 + 22v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-22v' to each side of the equation. 43 + -22v = -1 + 22v + -22v Combine like terms: 22v + -22v = 0 43 + -22v = -1 + 0 43 + -22v = -1 Add '-43' to each side of the equation. 43 + -43 + -22v = -1 + -43 Combine like terms: 43 + -43 = 0 0 + -22v = -1 + -43 -22v = -1 + -43 Combine like terms: -1 + -43 = -44 -22v = -44 Divide each side by '-22'. v = 2 Simplifying v = 2
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