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Simplifying 7(3v + -7) = 35 + 7v Reorder the terms: 7(-7 + 3v) = 35 + 7v (-7 * 7 + 3v * 7) = 35 + 7v (-49 + 21v) = 35 + 7v Solving -49 + 21v = 35 + 7v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7v' to each side of the equation. -49 + 21v + -7v = 35 + 7v + -7v Combine like terms: 21v + -7v = 14v -49 + 14v = 35 + 7v + -7v Combine like terms: 7v + -7v = 0 -49 + 14v = 35 + 0 -49 + 14v = 35 Add '49' to each side of the equation. -49 + 49 + 14v = 35 + 49 Combine like terms: -49 + 49 = 0 0 + 14v = 35 + 49 14v = 35 + 49 Combine like terms: 35 + 49 = 84 14v = 84 Divide each side by '14'. v = 6 Simplifying v = 6
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