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Simplifying 8(6 + 3v) + -6(v + 6) = 5v + 7v (6 * 8 + 3v * 8) + -6(v + 6) = 5v + 7v (48 + 24v) + -6(v + 6) = 5v + 7v Reorder the terms: 48 + 24v + -6(6 + v) = 5v + 7v 48 + 24v + (6 * -6 + v * -6) = 5v + 7v 48 + 24v + (-36 + -6v) = 5v + 7v Reorder the terms: 48 + -36 + 24v + -6v = 5v + 7v Combine like terms: 48 + -36 = 12 12 + 24v + -6v = 5v + 7v Combine like terms: 24v + -6v = 18v 12 + 18v = 5v + 7v Combine like terms: 5v + 7v = 12v 12 + 18v = 12v Solving 12 + 18v = 12v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-12v' to each side of the equation. 12 + 18v + -12v = 12v + -12v Combine like terms: 18v + -12v = 6v 12 + 6v = 12v + -12v Combine like terms: 12v + -12v = 0 12 + 6v = 0 Add '-12' to each side of the equation. 12 + -12 + 6v = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6v = 0 + -12 6v = 0 + -12 Combine like terms: 0 + -12 = -12 6v = -12 Divide each side by '6'. v = -2 Simplifying v = -2
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