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Simplifying 4(v + 3) + -5(3v + -8) = 12 + -2(3v + 1) Reorder the terms: 4(3 + v) + -5(3v + -8) = 12 + -2(3v + 1) (3 * 4 + v * 4) + -5(3v + -8) = 12 + -2(3v + 1) (12 + 4v) + -5(3v + -8) = 12 + -2(3v + 1) Reorder the terms: 12 + 4v + -5(-8 + 3v) = 12 + -2(3v + 1) 12 + 4v + (-8 * -5 + 3v * -5) = 12 + -2(3v + 1) 12 + 4v + (40 + -15v) = 12 + -2(3v + 1) Reorder the terms: 12 + 40 + 4v + -15v = 12 + -2(3v + 1) Combine like terms: 12 + 40 = 52 52 + 4v + -15v = 12 + -2(3v + 1) Combine like terms: 4v + -15v = -11v 52 + -11v = 12 + -2(3v + 1) Reorder the terms: 52 + -11v = 12 + -2(1 + 3v) 52 + -11v = 12 + (1 * -2 + 3v * -2) 52 + -11v = 12 + (-2 + -6v) Combine like terms: 12 + -2 = 10 52 + -11v = 10 + -6v Solving 52 + -11v = 10 + -6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '6v' to each side of the equation. 52 + -11v + 6v = 10 + -6v + 6v Combine like terms: -11v + 6v = -5v 52 + -5v = 10 + -6v + 6v Combine like terms: -6v + 6v = 0 52 + -5v = 10 + 0 52 + -5v = 10 Add '-52' to each side of the equation. 52 + -52 + -5v = 10 + -52 Combine like terms: 52 + -52 = 0 0 + -5v = 10 + -52 -5v = 10 + -52 Combine like terms: 10 + -52 = -42 -5v = -42 Divide each side by '-5'. v = 8.4 Simplifying v = 8.4
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