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Simplifying -7(v + 4) + 4v + 5 = 6v + 7 Reorder the terms: -7(4 + v) + 4v + 5 = 6v + 7 (4 * -7 + v * -7) + 4v + 5 = 6v + 7 (-28 + -7v) + 4v + 5 = 6v + 7 Reorder the terms: -28 + 5 + -7v + 4v = 6v + 7 Combine like terms: -28 + 5 = -23 -23 + -7v + 4v = 6v + 7 Combine like terms: -7v + 4v = -3v -23 + -3v = 6v + 7 Reorder the terms: -23 + -3v = 7 + 6v Solving -23 + -3v = 7 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. -23 + -3v + -6v = 7 + 6v + -6v Combine like terms: -3v + -6v = -9v -23 + -9v = 7 + 6v + -6v Combine like terms: 6v + -6v = 0 -23 + -9v = 7 + 0 -23 + -9v = 7 Add '23' to each side of the equation. -23 + 23 + -9v = 7 + 23 Combine like terms: -23 + 23 = 0 0 + -9v = 7 + 23 -9v = 7 + 23 Combine like terms: 7 + 23 = 30 -9v = 30 Divide each side by '-9'. v = -3.333333333 Simplifying v = -3.333333333
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