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Simplifying 4(2v + -1) + 2(2v + -3) = 5(2v + -4) Reorder the terms: 4(-1 + 2v) + 2(2v + -3) = 5(2v + -4) (-1 * 4 + 2v * 4) + 2(2v + -3) = 5(2v + -4) (-4 + 8v) + 2(2v + -3) = 5(2v + -4) Reorder the terms: -4 + 8v + 2(-3 + 2v) = 5(2v + -4) -4 + 8v + (-3 * 2 + 2v * 2) = 5(2v + -4) -4 + 8v + (-6 + 4v) = 5(2v + -4) Reorder the terms: -4 + -6 + 8v + 4v = 5(2v + -4) Combine like terms: -4 + -6 = -10 -10 + 8v + 4v = 5(2v + -4) Combine like terms: 8v + 4v = 12v -10 + 12v = 5(2v + -4) Reorder the terms: -10 + 12v = 5(-4 + 2v) -10 + 12v = (-4 * 5 + 2v * 5) -10 + 12v = (-20 + 10v) Solving -10 + 12v = -20 + 10v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10v' to each side of the equation. -10 + 12v + -10v = -20 + 10v + -10v Combine like terms: 12v + -10v = 2v -10 + 2v = -20 + 10v + -10v Combine like terms: 10v + -10v = 0 -10 + 2v = -20 + 0 -10 + 2v = -20 Add '10' to each side of the equation. -10 + 10 + 2v = -20 + 10 Combine like terms: -10 + 10 = 0 0 + 2v = -20 + 10 2v = -20 + 10 Combine like terms: -20 + 10 = -10 2v = -10 Divide each side by '2'. v = -5 Simplifying v = -5
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