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Simplifying 6(3v + -7) = 3(4v + 8) Reorder the terms: 6(-7 + 3v) = 3(4v + 8) (-7 * 6 + 3v * 6) = 3(4v + 8) (-42 + 18v) = 3(4v + 8) Reorder the terms: -42 + 18v = 3(8 + 4v) -42 + 18v = (8 * 3 + 4v * 3) -42 + 18v = (24 + 12v) Solving -42 + 18v = 24 + 12v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12v' to each side of the equation. -42 + 18v + -12v = 24 + 12v + -12v Combine like terms: 18v + -12v = 6v -42 + 6v = 24 + 12v + -12v Combine like terms: 12v + -12v = 0 -42 + 6v = 24 + 0 -42 + 6v = 24 Add '42' to each side of the equation. -42 + 42 + 6v = 24 + 42 Combine like terms: -42 + 42 = 0 0 + 6v = 24 + 42 6v = 24 + 42 Combine like terms: 24 + 42 = 66 6v = 66 Divide each side by '6'. v = 11 Simplifying v = 11
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