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Simplifying 3v + 12 + -10v = -23 + -31v + -5 Reorder the terms: 12 + 3v + -10v = -23 + -31v + -5 Combine like terms: 3v + -10v = -7v 12 + -7v = -23 + -31v + -5 Reorder the terms: 12 + -7v = -23 + -5 + -31v Combine like terms: -23 + -5 = -28 12 + -7v = -28 + -31v Solving 12 + -7v = -28 + -31v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '31v' to each side of the equation. 12 + -7v + 31v = -28 + -31v + 31v Combine like terms: -7v + 31v = 24v 12 + 24v = -28 + -31v + 31v Combine like terms: -31v + 31v = 0 12 + 24v = -28 + 0 12 + 24v = -28 Add '-12' to each side of the equation. 12 + -12 + 24v = -28 + -12 Combine like terms: 12 + -12 = 0 0 + 24v = -28 + -12 24v = -28 + -12 Combine like terms: -28 + -12 = -40 24v = -40 Divide each side by '24'. v = -1.666666667 Simplifying v = -1.666666667
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