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Simplifying 12 + 4(v + 2) = 8 + -2(v + 3y) Reorder the terms: 12 + 4(2 + v) = 8 + -2(v + 3y) 12 + (2 * 4 + v * 4) = 8 + -2(v + 3y) 12 + (8 + 4v) = 8 + -2(v + 3y) Combine like terms: 12 + 8 = 20 20 + 4v = 8 + -2(v + 3y) 20 + 4v = 8 + (v * -2 + 3y * -2) 20 + 4v = 8 + (-2v + -6y) Solving 20 + 4v = 8 + -2v + -6y 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. 20 + 4v + 2v = 8 + -2v + 2v + -6y Combine like terms: 4v + 2v = 6v 20 + 6v = 8 + -2v + 2v + -6y Combine like terms: -2v + 2v = 0 20 + 6v = 8 + 0 + -6y 20 + 6v = 8 + -6y Add '-20' to each side of the equation. 20 + -20 + 6v = 8 + -20 + -6y Combine like terms: 20 + -20 = 0 0 + 6v = 8 + -20 + -6y 6v = 8 + -20 + -6y Combine like terms: 8 + -20 = -12 6v = -12 + -6y Divide each side by '6'. v = -2 + -1y Simplifying v = -2 + -1y
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