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Simplifying 12v + 12 + 5v + -9 = -1(6v + 9) + 5(1 + 6v) Reorder the terms: 12 + -9 + 12v + 5v = -1(6v + 9) + 5(1 + 6v) Combine like terms: 12 + -9 = 3 3 + 12v + 5v = -1(6v + 9) + 5(1 + 6v) Combine like terms: 12v + 5v = 17v 3 + 17v = -1(6v + 9) + 5(1 + 6v) Reorder the terms: 3 + 17v = -1(9 + 6v) + 5(1 + 6v) 3 + 17v = (9 * -1 + 6v * -1) + 5(1 + 6v) 3 + 17v = (-9 + -6v) + 5(1 + 6v) 3 + 17v = -9 + -6v + (1 * 5 + 6v * 5) 3 + 17v = -9 + -6v + (5 + 30v) Reorder the terms: 3 + 17v = -9 + 5 + -6v + 30v Combine like terms: -9 + 5 = -4 3 + 17v = -4 + -6v + 30v Combine like terms: -6v + 30v = 24v 3 + 17v = -4 + 24v Solving 3 + 17v = -4 + 24v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-24v' to each side of the equation. 3 + 17v + -24v = -4 + 24v + -24v Combine like terms: 17v + -24v = -7v 3 + -7v = -4 + 24v + -24v Combine like terms: 24v + -24v = 0 3 + -7v = -4 + 0 3 + -7v = -4 Add '-3' to each side of the equation. 3 + -3 + -7v = -4 + -3 Combine like terms: 3 + -3 = 0 0 + -7v = -4 + -3 -7v = -4 + -3 Combine like terms: -4 + -3 = -7 -7v = -7 Divide each side by '-7'. v = 1 Simplifying v = 1
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