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Simplifying 7 + 2(4v + -6) = -3(5v + -1) + 7v Reorder the terms: 7 + 2(-6 + 4v) = -3(5v + -1) + 7v 7 + (-6 * 2 + 4v * 2) = -3(5v + -1) + 7v 7 + (-12 + 8v) = -3(5v + -1) + 7v Combine like terms: 7 + -12 = -5 -5 + 8v = -3(5v + -1) + 7v Reorder the terms: -5 + 8v = -3(-1 + 5v) + 7v -5 + 8v = (-1 * -3 + 5v * -3) + 7v -5 + 8v = (3 + -15v) + 7v Combine like terms: -15v + 7v = -8v -5 + 8v = 3 + -8v Solving -5 + 8v = 3 + -8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '8v' to each side of the equation. -5 + 8v + 8v = 3 + -8v + 8v Combine like terms: 8v + 8v = 16v -5 + 16v = 3 + -8v + 8v Combine like terms: -8v + 8v = 0 -5 + 16v = 3 + 0 -5 + 16v = 3 Add '5' to each side of the equation. -5 + 5 + 16v = 3 + 5 Combine like terms: -5 + 5 = 0 0 + 16v = 3 + 5 16v = 3 + 5 Combine like terms: 3 + 5 = 8 16v = 8 Divide each side by '16'. v = 0.5 Simplifying v = 0.5
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