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Simplifying 2(5v + -3) + -7(v + 1) = 7v + -5v Reorder the terms: 2(-3 + 5v) + -7(v + 1) = 7v + -5v (-3 * 2 + 5v * 2) + -7(v + 1) = 7v + -5v (-6 + 10v) + -7(v + 1) = 7v + -5v Reorder the terms: -6 + 10v + -7(1 + v) = 7v + -5v -6 + 10v + (1 * -7 + v * -7) = 7v + -5v -6 + 10v + (-7 + -7v) = 7v + -5v Reorder the terms: -6 + -7 + 10v + -7v = 7v + -5v Combine like terms: -6 + -7 = -13 -13 + 10v + -7v = 7v + -5v Combine like terms: 10v + -7v = 3v -13 + 3v = 7v + -5v Combine like terms: 7v + -5v = 2v -13 + 3v = 2v Solving -13 + 3v = 2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2v' to each side of the equation. -13 + 3v + -2v = 2v + -2v Combine like terms: 3v + -2v = 1v -13 + 1v = 2v + -2v Combine like terms: 2v + -2v = 0 -13 + 1v = 0 Add '13' to each side of the equation. -13 + 13 + 1v = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 1v = 0 + 13 1v = 0 + 13 Combine like terms: 0 + 13 = 13 1v = 13 Divide each side by '1'. v = 13 Simplifying v = 13
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