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Simplifying (v + -7) * 3 + 5(v + 1) = 2 + 5v Reorder the terms: (-7 + v) * 3 + 5(v + 1) = 2 + 5v Reorder the terms for easier multiplication: 3(-7 + v) + 5(v + 1) = 2 + 5v (-7 * 3 + v * 3) + 5(v + 1) = 2 + 5v (-21 + 3v) + 5(v + 1) = 2 + 5v Reorder the terms: -21 + 3v + 5(1 + v) = 2 + 5v -21 + 3v + (1 * 5 + v * 5) = 2 + 5v -21 + 3v + (5 + 5v) = 2 + 5v Reorder the terms: -21 + 5 + 3v + 5v = 2 + 5v Combine like terms: -21 + 5 = -16 -16 + 3v + 5v = 2 + 5v Combine like terms: 3v + 5v = 8v -16 + 8v = 2 + 5v Solving -16 + 8v = 2 + 5v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5v' to each side of the equation. -16 + 8v + -5v = 2 + 5v + -5v Combine like terms: 8v + -5v = 3v -16 + 3v = 2 + 5v + -5v Combine like terms: 5v + -5v = 0 -16 + 3v = 2 + 0 -16 + 3v = 2 Add '16' to each side of the equation. -16 + 16 + 3v = 2 + 16 Combine like terms: -16 + 16 = 0 0 + 3v = 2 + 16 3v = 2 + 16 Combine like terms: 2 + 16 = 18 3v = 18 Divide each side by '3'. v = 6 Simplifying v = 6
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