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Simplifying -7(v + 3) + 3v + 6 = 7v + 12 Reorder the terms: -7(3 + v) + 3v + 6 = 7v + 12 (3 * -7 + v * -7) + 3v + 6 = 7v + 12 (-21 + -7v) + 3v + 6 = 7v + 12 Reorder the terms: -21 + 6 + -7v + 3v = 7v + 12 Combine like terms: -21 + 6 = -15 -15 + -7v + 3v = 7v + 12 Combine like terms: -7v + 3v = -4v -15 + -4v = 7v + 12 Reorder the terms: -15 + -4v = 12 + 7v Solving -15 + -4v = 12 + 7v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7v' to each side of the equation. -15 + -4v + -7v = 12 + 7v + -7v Combine like terms: -4v + -7v = -11v -15 + -11v = 12 + 7v + -7v Combine like terms: 7v + -7v = 0 -15 + -11v = 12 + 0 -15 + -11v = 12 Add '15' to each side of the equation. -15 + 15 + -11v = 12 + 15 Combine like terms: -15 + 15 = 0 0 + -11v = 12 + 15 -11v = 12 + 15 Combine like terms: 12 + 15 = 27 -11v = 27 Divide each side by '-11'. v = -2.454545455 Simplifying v = -2.454545455
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