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Simplifying -9(v + 3) + 2v + 6 = 5v + 12 Reorder the terms: -9(3 + v) + 2v + 6 = 5v + 12 (3 * -9 + v * -9) + 2v + 6 = 5v + 12 (-27 + -9v) + 2v + 6 = 5v + 12 Reorder the terms: -27 + 6 + -9v + 2v = 5v + 12 Combine like terms: -27 + 6 = -21 -21 + -9v + 2v = 5v + 12 Combine like terms: -9v + 2v = -7v -21 + -7v = 5v + 12 Reorder the terms: -21 + -7v = 12 + 5v Solving -21 + -7v = 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. -21 + -7v + -5v = 12 + 5v + -5v Combine like terms: -7v + -5v = -12v -21 + -12v = 12 + 5v + -5v Combine like terms: 5v + -5v = 0 -21 + -12v = 12 + 0 -21 + -12v = 12 Add '21' to each side of the equation. -21 + 21 + -12v = 12 + 21 Combine like terms: -21 + 21 = 0 0 + -12v = 12 + 21 -12v = 12 + 21 Combine like terms: 12 + 21 = 33 -12v = 33 Divide each side by '-12'. v = -2.75 Simplifying v = -2.75
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