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Simplifying 3(1 + 4v) = -3v + 6(4 + 3v) (1 * 3 + 4v * 3) = -3v + 6(4 + 3v) (3 + 12v) = -3v + 6(4 + 3v) 3 + 12v = -3v + (4 * 6 + 3v * 6) 3 + 12v = -3v + (24 + 18v) Reorder the terms: 3 + 12v = 24 + -3v + 18v Combine like terms: -3v + 18v = 15v 3 + 12v = 24 + 15v Solving 3 + 12v = 24 + 15v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-15v' to each side of the equation. 3 + 12v + -15v = 24 + 15v + -15v Combine like terms: 12v + -15v = -3v 3 + -3v = 24 + 15v + -15v Combine like terms: 15v + -15v = 0 3 + -3v = 24 + 0 3 + -3v = 24 Add '-3' to each side of the equation. 3 + -3 + -3v = 24 + -3 Combine like terms: 3 + -3 = 0 0 + -3v = 24 + -3 -3v = 24 + -3 Combine like terms: 24 + -3 = 21 -3v = 21 Divide each side by '-3'. v = -7 Simplifying v = -7
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