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