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Simplifying 8v + -7(1 + 2v) = -31 + 2v 8v + (1 * -7 + 2v * -7) = -31 + 2v 8v + (-7 + -14v) = -31 + 2v Reorder the terms: -7 + 8v + -14v = -31 + 2v Combine like terms: 8v + -14v = -6v -7 + -6v = -31 + 2v Solving -7 + -6v = -31 + 2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2v' to each side of the equation. -7 + -6v + -2v = -31 + 2v + -2v Combine like terms: -6v + -2v = -8v -7 + -8v = -31 + 2v + -2v Combine like terms: 2v + -2v = 0 -7 + -8v = -31 + 0 -7 + -8v = -31 Add '7' to each side of the equation. -7 + 7 + -8v = -31 + 7 Combine like terms: -7 + 7 = 0 0 + -8v = -31 + 7 -8v = -31 + 7 Combine like terms: -31 + 7 = -24 -8v = -24 Divide each side by '-8'. v = 3 Simplifying v = 3
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