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Simplifying -6(v + 1) + 3(2v + 3) = v + (3v + 27) Reorder the terms: -6(1 + v) + 3(2v + 3) = v + (3v + 27) (1 * -6 + v * -6) + 3(2v + 3) = v + (3v + 27) (-6 + -6v) + 3(2v + 3) = v + (3v + 27) Reorder the terms: -6 + -6v + 3(3 + 2v) = v + (3v + 27) -6 + -6v + (3 * 3 + 2v * 3) = v + (3v + 27) -6 + -6v + (9 + 6v) = v + (3v + 27) Reorder the terms: -6 + 9 + -6v + 6v = v + (3v + 27) Combine like terms: -6 + 9 = 3 3 + -6v + 6v = v + (3v + 27) Combine like terms: -6v + 6v = 0 3 + 0 = v + (3v + 27) 3 = v + (3v + 27) Reorder the terms: 3 = v + (27 + 3v) Remove parenthesis around (27 + 3v) 3 = v + 27 + 3v Reorder the terms: 3 = 27 + v + 3v Combine like terms: v + 3v = 4v 3 = 27 + 4v Solving 3 = 27 + 4v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4v' to each side of the equation. 3 + -4v = 27 + 4v + -4v Combine like terms: 4v + -4v = 0 3 + -4v = 27 + 0 3 + -4v = 27 Add '-3' to each side of the equation. 3 + -3 + -4v = 27 + -3 Combine like terms: 3 + -3 = 0 0 + -4v = 27 + -3 -4v = 27 + -3 Combine like terms: 27 + -3 = 24 -4v = 24 Divide each side by '-4'. v = -6 Simplifying v = -6
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