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Simplifying (15 + v)(7) = (15 + -1v)(23) Reorder the terms for easier multiplication: 7(15 + v) = (15 + -1v)(23) (15 * 7 + v * 7) = (15 + -1v)(23) (105 + 7v) = (15 + -1v)(23) Reorder the terms for easier multiplication: 105 + 7v = 23(15 + -1v) 105 + 7v = (15 * 23 + -1v * 23) 105 + 7v = (345 + -23v) Solving 105 + 7v = 345 + -23v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '23v' to each side of the equation. 105 + 7v + 23v = 345 + -23v + 23v Combine like terms: 7v + 23v = 30v 105 + 30v = 345 + -23v + 23v Combine like terms: -23v + 23v = 0 105 + 30v = 345 + 0 105 + 30v = 345 Add '-105' to each side of the equation. 105 + -105 + 30v = 345 + -105 Combine like terms: 105 + -105 = 0 0 + 30v = 345 + -105 30v = 345 + -105 Combine like terms: 345 + -105 = 240 30v = 240 Divide each side by '30'. v = 8 Simplifying v = 8
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