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Simplifying 7(3 + 2v) + 2(-8v + -8) = 1 + -8v + 8v + -8 (3 * 7 + 2v * 7) + 2(-8v + -8) = 1 + -8v + 8v + -8 (21 + 14v) + 2(-8v + -8) = 1 + -8v + 8v + -8 Reorder the terms: 21 + 14v + 2(-8 + -8v) = 1 + -8v + 8v + -8 21 + 14v + (-8 * 2 + -8v * 2) = 1 + -8v + 8v + -8 21 + 14v + (-16 + -16v) = 1 + -8v + 8v + -8 Reorder the terms: 21 + -16 + 14v + -16v = 1 + -8v + 8v + -8 Combine like terms: 21 + -16 = 5 5 + 14v + -16v = 1 + -8v + 8v + -8 Combine like terms: 14v + -16v = -2v 5 + -2v = 1 + -8v + 8v + -8 Reorder the terms: 5 + -2v = 1 + -8 + -8v + 8v Combine like terms: 1 + -8 = -7 5 + -2v = -7 + -8v + 8v Combine like terms: -8v + 8v = 0 5 + -2v = -7 + 0 5 + -2v = -7 Solving 5 + -2v = -7 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2v = -7 + -5 Combine like terms: 5 + -5 = 0 0 + -2v = -7 + -5 -2v = -7 + -5 Combine like terms: -7 + -5 = -12 -2v = -12 Divide each side by '-2'. v = 6 Simplifying v = 6
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