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Simplifying 4(3v + -3) + 7v + 4 = 6(v + 6) + 2v Reorder the terms: 4(-3 + 3v) + 7v + 4 = 6(v + 6) + 2v (-3 * 4 + 3v * 4) + 7v + 4 = 6(v + 6) + 2v (-12 + 12v) + 7v + 4 = 6(v + 6) + 2v Reorder the terms: -12 + 4 + 12v + 7v = 6(v + 6) + 2v Combine like terms: -12 + 4 = -8 -8 + 12v + 7v = 6(v + 6) + 2v Combine like terms: 12v + 7v = 19v -8 + 19v = 6(v + 6) + 2v Reorder the terms: -8 + 19v = 6(6 + v) + 2v -8 + 19v = (6 * 6 + v * 6) + 2v -8 + 19v = (36 + 6v) + 2v Combine like terms: 6v + 2v = 8v -8 + 19v = 36 + 8v Solving -8 + 19v = 36 + 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. -8 + 19v + -8v = 36 + 8v + -8v Combine like terms: 19v + -8v = 11v -8 + 11v = 36 + 8v + -8v Combine like terms: 8v + -8v = 0 -8 + 11v = 36 + 0 -8 + 11v = 36 Add '8' to each side of the equation. -8 + 8 + 11v = 36 + 8 Combine like terms: -8 + 8 = 0 0 + 11v = 36 + 8 11v = 36 + 8 Combine like terms: 36 + 8 = 44 11v = 44 Divide each side by '11'. v = 4 Simplifying v = 4
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