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Simplifying -7(v + 3) + 4v + 6 = 6v + 7 Reorder the terms: -7(3 + v) + 4v + 6 = 6v + 7 (3 * -7 + v * -7) + 4v + 6 = 6v + 7 (-21 + -7v) + 4v + 6 = 6v + 7 Reorder the terms: -21 + 6 + -7v + 4v = 6v + 7 Combine like terms: -21 + 6 = -15 -15 + -7v + 4v = 6v + 7 Combine like terms: -7v + 4v = -3v -15 + -3v = 6v + 7 Reorder the terms: -15 + -3v = 7 + 6v Solving -15 + -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. -15 + -3v + -6v = 7 + 6v + -6v Combine like terms: -3v + -6v = -9v -15 + -9v = 7 + 6v + -6v Combine like terms: 6v + -6v = 0 -15 + -9v = 7 + 0 -15 + -9v = 7 Add '15' to each side of the equation. -15 + 15 + -9v = 7 + 15 Combine like terms: -15 + 15 = 0 0 + -9v = 7 + 15 -9v = 7 + 15 Combine like terms: 7 + 15 = 22 -9v = 22 Divide each side by '-9'. v = -2.444444444 Simplifying v = -2.444444444
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