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Simplifying 4(2v + 1) = 3(5v + -8) Reorder the terms: 4(1 + 2v) = 3(5v + -8) (1 * 4 + 2v * 4) = 3(5v + -8) (4 + 8v) = 3(5v + -8) Reorder the terms: 4 + 8v = 3(-8 + 5v) 4 + 8v = (-8 * 3 + 5v * 3) 4 + 8v = (-24 + 15v) Solving 4 + 8v = -24 + 15v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-15v' to each side of the equation. 4 + 8v + -15v = -24 + 15v + -15v Combine like terms: 8v + -15v = -7v 4 + -7v = -24 + 15v + -15v Combine like terms: 15v + -15v = 0 4 + -7v = -24 + 0 4 + -7v = -24 Add '-4' to each side of the equation. 4 + -4 + -7v = -24 + -4 Combine like terms: 4 + -4 = 0 0 + -7v = -24 + -4 -7v = -24 + -4 Combine like terms: -24 + -4 = -28 -7v = -28 Divide each side by '-7'. v = 4 Simplifying v = 4
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