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Simplifying 2(3v + 2) = 4[4v + -3(-1v + -4)] Reorder the terms: 2(2 + 3v) = 4[4v + -3(-1v + -4)] (2 * 2 + 3v * 2) = 4[4v + -3(-1v + -4)] (4 + 6v) = 4[4v + -3(-1v + -4)] Reorder the terms: 4 + 6v = 4[4v + -3(-4 + -1v)] 4 + 6v = 4[4v + (-4 * -3 + -1v * -3)] 4 + 6v = 4[4v + (12 + 3v)] Reorder the terms: 4 + 6v = 4[12 + 4v + 3v] Combine like terms: 4v + 3v = 7v 4 + 6v = 4[12 + 7v] 4 + 6v = [12 * 4 + 7v * 4] 4 + 6v = [48 + 28v] Solving 4 + 6v = 48 + 28v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-28v' to each side of the equation. 4 + 6v + -28v = 48 + 28v + -28v Combine like terms: 6v + -28v = -22v 4 + -22v = 48 + 28v + -28v Combine like terms: 28v + -28v = 0 4 + -22v = 48 + 0 4 + -22v = 48 Add '-4' to each side of the equation. 4 + -4 + -22v = 48 + -4 Combine like terms: 4 + -4 = 0 0 + -22v = 48 + -4 -22v = 48 + -4 Combine like terms: 48 + -4 = 44 -22v = 44 Divide each side by '-22'. v = -2 Simplifying v = -2
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