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Simplifying 8v + 33 = 2v + 5(3v + -6) Reorder the terms: 33 + 8v = 2v + 5(3v + -6) Reorder the terms: 33 + 8v = 2v + 5(-6 + 3v) 33 + 8v = 2v + (-6 * 5 + 3v * 5) 33 + 8v = 2v + (-30 + 15v) Reorder the terms: 33 + 8v = -30 + 2v + 15v Combine like terms: 2v + 15v = 17v 33 + 8v = -30 + 17v Solving 33 + 8v = -30 + 17v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-17v' to each side of the equation. 33 + 8v + -17v = -30 + 17v + -17v Combine like terms: 8v + -17v = -9v 33 + -9v = -30 + 17v + -17v Combine like terms: 17v + -17v = 0 33 + -9v = -30 + 0 33 + -9v = -30 Add '-33' to each side of the equation. 33 + -33 + -9v = -30 + -33 Combine like terms: 33 + -33 = 0 0 + -9v = -30 + -33 -9v = -30 + -33 Combine like terms: -30 + -33 = -63 -9v = -63 Divide each side by '-9'. v = 7 Simplifying v = 7
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