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Simplifying 5v + 8 + 4 + 6v = 5(1 + 6v) + 6(-4v + -8) Reorder the terms: 8 + 4 + 5v + 6v = 5(1 + 6v) + 6(-4v + -8) Combine like terms: 8 + 4 = 12 12 + 5v + 6v = 5(1 + 6v) + 6(-4v + -8) Combine like terms: 5v + 6v = 11v 12 + 11v = 5(1 + 6v) + 6(-4v + -8) 12 + 11v = (1 * 5 + 6v * 5) + 6(-4v + -8) 12 + 11v = (5 + 30v) + 6(-4v + -8) Reorder the terms: 12 + 11v = 5 + 30v + 6(-8 + -4v) 12 + 11v = 5 + 30v + (-8 * 6 + -4v * 6) 12 + 11v = 5 + 30v + (-48 + -24v) Reorder the terms: 12 + 11v = 5 + -48 + 30v + -24v Combine like terms: 5 + -48 = -43 12 + 11v = -43 + 30v + -24v Combine like terms: 30v + -24v = 6v 12 + 11v = -43 + 6v Solving 12 + 11v = -43 + 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. 12 + 11v + -6v = -43 + 6v + -6v Combine like terms: 11v + -6v = 5v 12 + 5v = -43 + 6v + -6v Combine like terms: 6v + -6v = 0 12 + 5v = -43 + 0 12 + 5v = -43 Add '-12' to each side of the equation. 12 + -12 + 5v = -43 + -12 Combine like terms: 12 + -12 = 0 0 + 5v = -43 + -12 5v = -43 + -12 Combine like terms: -43 + -12 = -55 5v = -55 Divide each side by '5'. v = -11 Simplifying v = -11
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