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Simplifying -7(v + 1) = -2(3v + -4) + 5v Reorder the terms: -7(1 + v) = -2(3v + -4) + 5v (1 * -7 + v * -7) = -2(3v + -4) + 5v (-7 + -7v) = -2(3v + -4) + 5v Reorder the terms: -7 + -7v = -2(-4 + 3v) + 5v -7 + -7v = (-4 * -2 + 3v * -2) + 5v -7 + -7v = (8 + -6v) + 5v Combine like terms: -6v + 5v = -1v -7 + -7v = 8 + -1v Solving -7 + -7v = 8 + -1v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add 'v' to each side of the equation. -7 + -7v + v = 8 + -1v + v Combine like terms: -7v + v = -6v -7 + -6v = 8 + -1v + v Combine like terms: -1v + v = 0 -7 + -6v = 8 + 0 -7 + -6v = 8 Add '7' to each side of the equation. -7 + 7 + -6v = 8 + 7 Combine like terms: -7 + 7 = 0 0 + -6v = 8 + 7 -6v = 8 + 7 Combine like terms: 8 + 7 = 15 -6v = 15 Divide each side by '-6'. v = -2.5 Simplifying v = -2.5
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