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Simplifying 5(2v + 1) = 7v + 4(3 + -1v) Reorder the terms: 5(1 + 2v) = 7v + 4(3 + -1v) (1 * 5 + 2v * 5) = 7v + 4(3 + -1v) (5 + 10v) = 7v + 4(3 + -1v) 5 + 10v = 7v + (3 * 4 + -1v * 4) 5 + 10v = 7v + (12 + -4v) Reorder the terms: 5 + 10v = 12 + 7v + -4v Combine like terms: 7v + -4v = 3v 5 + 10v = 12 + 3v Solving 5 + 10v = 12 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. 5 + 10v + -3v = 12 + 3v + -3v Combine like terms: 10v + -3v = 7v 5 + 7v = 12 + 3v + -3v Combine like terms: 3v + -3v = 0 5 + 7v = 12 + 0 5 + 7v = 12 Add '-5' to each side of the equation. 5 + -5 + 7v = 12 + -5 Combine like terms: 5 + -5 = 0 0 + 7v = 12 + -5 7v = 12 + -5 Combine like terms: 12 + -5 = 7 7v = 7 Divide each side by '7'. v = 1 Simplifying v = 1
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