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Simplifying 12 + -1(7v + -6) + 10v = 3(2v + 7) Reorder the terms: 12 + -1(-6 + 7v) + 10v = 3(2v + 7) 12 + (-6 * -1 + 7v * -1) + 10v = 3(2v + 7) 12 + (6 + -7v) + 10v = 3(2v + 7) Combine like terms: 12 + 6 = 18 18 + -7v + 10v = 3(2v + 7) Combine like terms: -7v + 10v = 3v 18 + 3v = 3(2v + 7) Reorder the terms: 18 + 3v = 3(7 + 2v) 18 + 3v = (7 * 3 + 2v * 3) 18 + 3v = (21 + 6v) Solving 18 + 3v = 21 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. 18 + 3v + -6v = 21 + 6v + -6v Combine like terms: 3v + -6v = -3v 18 + -3v = 21 + 6v + -6v Combine like terms: 6v + -6v = 0 18 + -3v = 21 + 0 18 + -3v = 21 Add '-18' to each side of the equation. 18 + -18 + -3v = 21 + -18 Combine like terms: 18 + -18 = 0 0 + -3v = 21 + -18 -3v = 21 + -18 Combine like terms: 21 + -18 = 3 -3v = 3 Divide each side by '-3'. v = -1 Simplifying v = -1
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