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Simplifying (3v + 2) + -1(v + 1) = v + (2v + 3) Reorder the terms: (2 + 3v) + -1(v + 1) = v + (2v + 3) Remove parenthesis around (2 + 3v) 2 + 3v + -1(v + 1) = v + (2v + 3) Reorder the terms: 2 + 3v + -1(1 + v) = v + (2v + 3) 2 + 3v + (1 * -1 + v * -1) = v + (2v + 3) 2 + 3v + (-1 + -1v) = v + (2v + 3) Reorder the terms: 2 + -1 + 3v + -1v = v + (2v + 3) Combine like terms: 2 + -1 = 1 1 + 3v + -1v = v + (2v + 3) Combine like terms: 3v + -1v = 2v 1 + 2v = v + (2v + 3) Reorder the terms: 1 + 2v = v + (3 + 2v) Remove parenthesis around (3 + 2v) 1 + 2v = v + 3 + 2v Reorder the terms: 1 + 2v = 3 + v + 2v Combine like terms: v + 2v = 3v 1 + 2v = 3 + 3v Solving 1 + 2v = 3 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. 1 + 2v + -3v = 3 + 3v + -3v Combine like terms: 2v + -3v = -1v 1 + -1v = 3 + 3v + -3v Combine like terms: 3v + -3v = 0 1 + -1v = 3 + 0 1 + -1v = 3 Add '-1' to each side of the equation. 1 + -1 + -1v = 3 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 3 + -1 -1v = 3 + -1 Combine like terms: 3 + -1 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2
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