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Simplifying 31 + 8v = -1 + 7(3v + -1) Reorder the terms: 31 + 8v = -1 + 7(-1 + 3v) 31 + 8v = -1 + (-1 * 7 + 3v * 7) 31 + 8v = -1 + (-7 + 21v) Combine like terms: -1 + -7 = -8 31 + 8v = -8 + 21v Solving 31 + 8v = -8 + 21v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-21v' to each side of the equation. 31 + 8v + -21v = -8 + 21v + -21v Combine like terms: 8v + -21v = -13v 31 + -13v = -8 + 21v + -21v Combine like terms: 21v + -21v = 0 31 + -13v = -8 + 0 31 + -13v = -8 Add '-31' to each side of the equation. 31 + -31 + -13v = -8 + -31 Combine like terms: 31 + -31 = 0 0 + -13v = -8 + -31 -13v = -8 + -31 Combine like terms: -8 + -31 = -39 -13v = -39 Divide each side by '-13'. v = 3 Simplifying v = 3
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