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Simplifying 31 = 5v + 6(v + 7) Reorder the terms: 31 = 5v + 6(7 + v) 31 = 5v + (7 * 6 + v * 6) 31 = 5v + (42 + 6v) Reorder the terms: 31 = 42 + 5v + 6v Combine like terms: 5v + 6v = 11v 31 = 42 + 11v Solving 31 = 42 + 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. 31 + -11v = 42 + 11v + -11v Combine like terms: 11v + -11v = 0 31 + -11v = 42 + 0 31 + -11v = 42 Add '-31' to each side of the equation. 31 + -31 + -11v = 42 + -31 Combine like terms: 31 + -31 = 0 0 + -11v = 42 + -31 -11v = 42 + -31 Combine like terms: 42 + -31 = 11 -11v = 11 Divide each side by '-11'. v = -1 Simplifying v = -1
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