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Simplifying 7(v + 4) + 2v + 5 = 7v + 12 Reorder the terms: 7(4 + v) + 2v + 5 = 7v + 12 (4 * 7 + v * 7) + 2v + 5 = 7v + 12 (28 + 7v) + 2v + 5 = 7v + 12 Reorder the terms: 28 + 5 + 7v + 2v = 7v + 12 Combine like terms: 28 + 5 = 33 33 + 7v + 2v = 7v + 12 Combine like terms: 7v + 2v = 9v 33 + 9v = 7v + 12 Reorder the terms: 33 + 9v = 12 + 7v Solving 33 + 9v = 12 + 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. 33 + 9v + -7v = 12 + 7v + -7v Combine like terms: 9v + -7v = 2v 33 + 2v = 12 + 7v + -7v Combine like terms: 7v + -7v = 0 33 + 2v = 12 + 0 33 + 2v = 12 Add '-33' to each side of the equation. 33 + -33 + 2v = 12 + -33 Combine like terms: 33 + -33 = 0 0 + 2v = 12 + -33 2v = 12 + -33 Combine like terms: 12 + -33 = -21 2v = -21 Divide each side by '2'. v = -10.5 Simplifying v = -10.5
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