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Simplifying 3(v + 1) = -3v + 45 Reorder the terms: 3(1 + v) = -3v + 45 (1 * 3 + v * 3) = -3v + 45 (3 + 3v) = -3v + 45 Reorder the terms: 3 + 3v = 45 + -3v Solving 3 + 3v = 45 + -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. 3 + 3v + 3v = 45 + -3v + 3v Combine like terms: 3v + 3v = 6v 3 + 6v = 45 + -3v + 3v Combine like terms: -3v + 3v = 0 3 + 6v = 45 + 0 3 + 6v = 45 Add '-3' to each side of the equation. 3 + -3 + 6v = 45 + -3 Combine like terms: 3 + -3 = 0 0 + 6v = 45 + -3 6v = 45 + -3 Combine like terms: 45 + -3 = 42 6v = 42 Divide each side by '6'. v = 7 Simplifying v = 7
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