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Simplifying -7(v + 4) + 3v + 6 = 5v + 9 Reorder the terms: -7(4 + v) + 3v + 6 = 5v + 9 (4 * -7 + v * -7) + 3v + 6 = 5v + 9 (-28 + -7v) + 3v + 6 = 5v + 9 Reorder the terms: -28 + 6 + -7v + 3v = 5v + 9 Combine like terms: -28 + 6 = -22 -22 + -7v + 3v = 5v + 9 Combine like terms: -7v + 3v = -4v -22 + -4v = 5v + 9 Reorder the terms: -22 + -4v = 9 + 5v Solving -22 + -4v = 9 + 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. -22 + -4v + -5v = 9 + 5v + -5v Combine like terms: -4v + -5v = -9v -22 + -9v = 9 + 5v + -5v Combine like terms: 5v + -5v = 0 -22 + -9v = 9 + 0 -22 + -9v = 9 Add '22' to each side of the equation. -22 + 22 + -9v = 9 + 22 Combine like terms: -22 + 22 = 0 0 + -9v = 9 + 22 -9v = 9 + 22 Combine like terms: 9 + 22 = 31 -9v = 31 Divide each side by '-9'. v = -3.444444444 Simplifying v = -3.444444444
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