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Simplifying -9(v + 3) + 2v + 6 = 8v + 7 Reorder the terms: -9(3 + v) + 2v + 6 = 8v + 7 (3 * -9 + v * -9) + 2v + 6 = 8v + 7 (-27 + -9v) + 2v + 6 = 8v + 7 Reorder the terms: -27 + 6 + -9v + 2v = 8v + 7 Combine like terms: -27 + 6 = -21 -21 + -9v + 2v = 8v + 7 Combine like terms: -9v + 2v = -7v -21 + -7v = 8v + 7 Reorder the terms: -21 + -7v = 7 + 8v Solving -21 + -7v = 7 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. -21 + -7v + -8v = 7 + 8v + -8v Combine like terms: -7v + -8v = -15v -21 + -15v = 7 + 8v + -8v Combine like terms: 8v + -8v = 0 -21 + -15v = 7 + 0 -21 + -15v = 7 Add '21' to each side of the equation. -21 + 21 + -15v = 7 + 21 Combine like terms: -21 + 21 = 0 0 + -15v = 7 + 21 -15v = 7 + 21 Combine like terms: 7 + 21 = 28 -15v = 28 Divide each side by '-15'. v = -1.866666667 Simplifying v = -1.866666667
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