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Simplifying 22 + 7v = 4v + 7(5v + -6) Reorder the terms: 22 + 7v = 4v + 7(-6 + 5v) 22 + 7v = 4v + (-6 * 7 + 5v * 7) 22 + 7v = 4v + (-42 + 35v) Reorder the terms: 22 + 7v = -42 + 4v + 35v Combine like terms: 4v + 35v = 39v 22 + 7v = -42 + 39v Solving 22 + 7v = -42 + 39v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-39v' to each side of the equation. 22 + 7v + -39v = -42 + 39v + -39v Combine like terms: 7v + -39v = -32v 22 + -32v = -42 + 39v + -39v Combine like terms: 39v + -39v = 0 22 + -32v = -42 + 0 22 + -32v = -42 Add '-22' to each side of the equation. 22 + -22 + -32v = -42 + -22 Combine like terms: 22 + -22 = 0 0 + -32v = -42 + -22 -32v = -42 + -22 Combine like terms: -42 + -22 = -64 -32v = -64 Divide each side by '-32'. v = 2 Simplifying v = 2
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