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Simplifying 3(4v + 1) + 3(2v + 3) = 2(v + -7) + 4 Reorder the terms: 3(1 + 4v) + 3(2v + 3) = 2(v + -7) + 4 (1 * 3 + 4v * 3) + 3(2v + 3) = 2(v + -7) + 4 (3 + 12v) + 3(2v + 3) = 2(v + -7) + 4 Reorder the terms: 3 + 12v + 3(3 + 2v) = 2(v + -7) + 4 3 + 12v + (3 * 3 + 2v * 3) = 2(v + -7) + 4 3 + 12v + (9 + 6v) = 2(v + -7) + 4 Reorder the terms: 3 + 9 + 12v + 6v = 2(v + -7) + 4 Combine like terms: 3 + 9 = 12 12 + 12v + 6v = 2(v + -7) + 4 Combine like terms: 12v + 6v = 18v 12 + 18v = 2(v + -7) + 4 Reorder the terms: 12 + 18v = 2(-7 + v) + 4 12 + 18v = (-7 * 2 + v * 2) + 4 12 + 18v = (-14 + 2v) + 4 Reorder the terms: 12 + 18v = -14 + 4 + 2v Combine like terms: -14 + 4 = -10 12 + 18v = -10 + 2v Solving 12 + 18v = -10 + 2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2v' to each side of the equation. 12 + 18v + -2v = -10 + 2v + -2v Combine like terms: 18v + -2v = 16v 12 + 16v = -10 + 2v + -2v Combine like terms: 2v + -2v = 0 12 + 16v = -10 + 0 12 + 16v = -10 Add '-12' to each side of the equation. 12 + -12 + 16v = -10 + -12 Combine like terms: 12 + -12 = 0 0 + 16v = -10 + -12 16v = -10 + -12 Combine like terms: -10 + -12 = -22 16v = -22 Divide each side by '16'. v = -1.375 Simplifying v = -1.375
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