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Simplifying 3(4 + -8v) = -3(1 + 7v) (4 * 3 + -8v * 3) = -3(1 + 7v) (12 + -24v) = -3(1 + 7v) 12 + -24v = (1 * -3 + 7v * -3) 12 + -24v = (-3 + -21v) Solving 12 + -24v = -3 + -21v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '21v' to each side of the equation. 12 + -24v + 21v = -3 + -21v + 21v Combine like terms: -24v + 21v = -3v 12 + -3v = -3 + -21v + 21v Combine like terms: -21v + 21v = 0 12 + -3v = -3 + 0 12 + -3v = -3 Add '-12' to each side of the equation. 12 + -12 + -3v = -3 + -12 Combine like terms: 12 + -12 = 0 0 + -3v = -3 + -12 -3v = -3 + -12 Combine like terms: -3 + -12 = -15 -3v = -15 Divide each side by '-3'. v = 5 Simplifying v = 5
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