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Simplifying -7(2v + 7) + 8(v + 3) = v + -2 + 5 Reorder the terms: -7(7 + 2v) + 8(v + 3) = v + -2 + 5 (7 * -7 + 2v * -7) + 8(v + 3) = v + -2 + 5 (-49 + -14v) + 8(v + 3) = v + -2 + 5 Reorder the terms: -49 + -14v + 8(3 + v) = v + -2 + 5 -49 + -14v + (3 * 8 + v * 8) = v + -2 + 5 -49 + -14v + (24 + 8v) = v + -2 + 5 Reorder the terms: -49 + 24 + -14v + 8v = v + -2 + 5 Combine like terms: -49 + 24 = -25 -25 + -14v + 8v = v + -2 + 5 Combine like terms: -14v + 8v = -6v -25 + -6v = v + -2 + 5 Reorder the terms: -25 + -6v = -2 + 5 + v Combine like terms: -2 + 5 = 3 -25 + -6v = 3 + v Solving -25 + -6v = 3 + v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1v' to each side of the equation. -25 + -6v + -1v = 3 + v + -1v Combine like terms: -6v + -1v = -7v -25 + -7v = 3 + v + -1v Combine like terms: v + -1v = 0 -25 + -7v = 3 + 0 -25 + -7v = 3 Add '25' to each side of the equation. -25 + 25 + -7v = 3 + 25 Combine like terms: -25 + 25 = 0 0 + -7v = 3 + 25 -7v = 3 + 25 Combine like terms: 3 + 25 = 28 -7v = 28 Divide each side by '-7'. v = -4 Simplifying v = -4
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