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Simplifying 5(6 + -1v) + 2v = 3(v + -4) (6 * 5 + -1v * 5) + 2v = 3(v + -4) (30 + -5v) + 2v = 3(v + -4) Combine like terms: -5v + 2v = -3v 30 + -3v = 3(v + -4) Reorder the terms: 30 + -3v = 3(-4 + v) 30 + -3v = (-4 * 3 + v * 3) 30 + -3v = (-12 + 3v) Solving 30 + -3v = -12 + 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. 30 + -3v + -3v = -12 + 3v + -3v Combine like terms: -3v + -3v = -6v 30 + -6v = -12 + 3v + -3v Combine like terms: 3v + -3v = 0 30 + -6v = -12 + 0 30 + -6v = -12 Add '-30' to each side of the equation. 30 + -30 + -6v = -12 + -30 Combine like terms: 30 + -30 = 0 0 + -6v = -12 + -30 -6v = -12 + -30 Combine like terms: -12 + -30 = -42 -6v = -42 Divide each side by '-6'. v = 7 Simplifying v = 7
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