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Simplifying 6(11v + -3) + -14 = 19 + 3v + 12 Reorder the terms: 6(-3 + 11v) + -14 = 19 + 3v + 12 (-3 * 6 + 11v * 6) + -14 = 19 + 3v + 12 (-18 + 66v) + -14 = 19 + 3v + 12 Reorder the terms: -18 + -14 + 66v = 19 + 3v + 12 Combine like terms: -18 + -14 = -32 -32 + 66v = 19 + 3v + 12 Reorder the terms: -32 + 66v = 19 + 12 + 3v Combine like terms: 19 + 12 = 31 -32 + 66v = 31 + 3v Solving -32 + 66v = 31 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. -32 + 66v + -3v = 31 + 3v + -3v Combine like terms: 66v + -3v = 63v -32 + 63v = 31 + 3v + -3v Combine like terms: 3v + -3v = 0 -32 + 63v = 31 + 0 -32 + 63v = 31 Add '32' to each side of the equation. -32 + 32 + 63v = 31 + 32 Combine like terms: -32 + 32 = 0 0 + 63v = 31 + 32 63v = 31 + 32 Combine like terms: 31 + 32 = 63 63v = 63 Divide each side by '63'. v = 1 Simplifying v = 1
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