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Simplifying 7(v + -5) + 2(4v + -7) = -34 Reorder the terms: 7(-5 + v) + 2(4v + -7) = -34 (-5 * 7 + v * 7) + 2(4v + -7) = -34 (-35 + 7v) + 2(4v + -7) = -34 Reorder the terms: -35 + 7v + 2(-7 + 4v) = -34 -35 + 7v + (-7 * 2 + 4v * 2) = -34 -35 + 7v + (-14 + 8v) = -34 Reorder the terms: -35 + -14 + 7v + 8v = -34 Combine like terms: -35 + -14 = -49 -49 + 7v + 8v = -34 Combine like terms: 7v + 8v = 15v -49 + 15v = -34 Solving -49 + 15v = -34 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + 15v = -34 + 49 Combine like terms: -49 + 49 = 0 0 + 15v = -34 + 49 15v = -34 + 49 Combine like terms: -34 + 49 = 15 15v = 15 Divide each side by '15'. v = 1 Simplifying v = 1
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