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Simplifying -7(v + 2) + 3v + 7 = 5v + 12 Reorder the terms: -7(2 + v) + 3v + 7 = 5v + 12 (2 * -7 + v * -7) + 3v + 7 = 5v + 12 (-14 + -7v) + 3v + 7 = 5v + 12 Reorder the terms: -14 + 7 + -7v + 3v = 5v + 12 Combine like terms: -14 + 7 = -7 -7 + -7v + 3v = 5v + 12 Combine like terms: -7v + 3v = -4v -7 + -4v = 5v + 12 Reorder the terms: -7 + -4v = 12 + 5v Solving -7 + -4v = 12 + 5v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5v' to each side of the equation. -7 + -4v + -5v = 12 + 5v + -5v Combine like terms: -4v + -5v = -9v -7 + -9v = 12 + 5v + -5v Combine like terms: 5v + -5v = 0 -7 + -9v = 12 + 0 -7 + -9v = 12 Add '7' to each side of the equation. -7 + 7 + -9v = 12 + 7 Combine like terms: -7 + 7 = 0 0 + -9v = 12 + 7 -9v = 12 + 7 Combine like terms: 12 + 7 = 19 -9v = 19 Divide each side by '-9'. v = -2.111111111 Simplifying v = -2.111111111
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