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Simplifying 5(v + 2) + v = 3(v + 1) + 1 Reorder the terms: 5(2 + v) + v = 3(v + 1) + 1 (2 * 5 + v * 5) + v = 3(v + 1) + 1 (10 + 5v) + v = 3(v + 1) + 1 Combine like terms: 5v + v = 6v 10 + 6v = 3(v + 1) + 1 Reorder the terms: 10 + 6v = 3(1 + v) + 1 10 + 6v = (1 * 3 + v * 3) + 1 10 + 6v = (3 + 3v) + 1 Reorder the terms: 10 + 6v = 3 + 1 + 3v Combine like terms: 3 + 1 = 4 10 + 6v = 4 + 3v Solving 10 + 6v = 4 + 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. 10 + 6v + -3v = 4 + 3v + -3v Combine like terms: 6v + -3v = 3v 10 + 3v = 4 + 3v + -3v Combine like terms: 3v + -3v = 0 10 + 3v = 4 + 0 10 + 3v = 4 Add '-10' to each side of the equation. 10 + -10 + 3v = 4 + -10 Combine like terms: 10 + -10 = 0 0 + 3v = 4 + -10 3v = 4 + -10 Combine like terms: 4 + -10 = -6 3v = -6 Divide each side by '3'. v = -2 Simplifying v = -2
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