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Simplifying 2(3v + 4) + 5(3v + -5) = 3(v + -7) + 8 Reorder the terms: 2(4 + 3v) + 5(3v + -5) = 3(v + -7) + 8 (4 * 2 + 3v * 2) + 5(3v + -5) = 3(v + -7) + 8 (8 + 6v) + 5(3v + -5) = 3(v + -7) + 8 Reorder the terms: 8 + 6v + 5(-5 + 3v) = 3(v + -7) + 8 8 + 6v + (-5 * 5 + 3v * 5) = 3(v + -7) + 8 8 + 6v + (-25 + 15v) = 3(v + -7) + 8 Reorder the terms: 8 + -25 + 6v + 15v = 3(v + -7) + 8 Combine like terms: 8 + -25 = -17 -17 + 6v + 15v = 3(v + -7) + 8 Combine like terms: 6v + 15v = 21v -17 + 21v = 3(v + -7) + 8 Reorder the terms: -17 + 21v = 3(-7 + v) + 8 -17 + 21v = (-7 * 3 + v * 3) + 8 -17 + 21v = (-21 + 3v) + 8 Reorder the terms: -17 + 21v = -21 + 8 + 3v Combine like terms: -21 + 8 = -13 -17 + 21v = -13 + 3v Solving -17 + 21v = -13 + 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. -17 + 21v + -3v = -13 + 3v + -3v Combine like terms: 21v + -3v = 18v -17 + 18v = -13 + 3v + -3v Combine like terms: 3v + -3v = 0 -17 + 18v = -13 + 0 -17 + 18v = -13 Add '17' to each side of the equation. -17 + 17 + 18v = -13 + 17 Combine like terms: -17 + 17 = 0 0 + 18v = -13 + 17 18v = -13 + 17 Combine like terms: -13 + 17 = 4 18v = 4 Divide each side by '18'. v = 0.2222222222 Simplifying v = 0.2222222222
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