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Simplifying v + 6 + v + 8 = 2(7 + -5v) + 4(5v + -8) Reorder the terms: 6 + 8 + v + v = 2(7 + -5v) + 4(5v + -8) Combine like terms: 6 + 8 = 14 14 + v + v = 2(7 + -5v) + 4(5v + -8) Combine like terms: v + v = 2v 14 + 2v = 2(7 + -5v) + 4(5v + -8) 14 + 2v = (7 * 2 + -5v * 2) + 4(5v + -8) 14 + 2v = (14 + -10v) + 4(5v + -8) Reorder the terms: 14 + 2v = 14 + -10v + 4(-8 + 5v) 14 + 2v = 14 + -10v + (-8 * 4 + 5v * 4) 14 + 2v = 14 + -10v + (-32 + 20v) Reorder the terms: 14 + 2v = 14 + -32 + -10v + 20v Combine like terms: 14 + -32 = -18 14 + 2v = -18 + -10v + 20v Combine like terms: -10v + 20v = 10v 14 + 2v = -18 + 10v Solving 14 + 2v = -18 + 10v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-10v' to each side of the equation. 14 + 2v + -10v = -18 + 10v + -10v Combine like terms: 2v + -10v = -8v 14 + -8v = -18 + 10v + -10v Combine like terms: 10v + -10v = 0 14 + -8v = -18 + 0 14 + -8v = -18 Add '-14' to each side of the equation. 14 + -14 + -8v = -18 + -14 Combine like terms: 14 + -14 = 0 0 + -8v = -18 + -14 -8v = -18 + -14 Combine like terms: -18 + -14 = -32 -8v = -32 Divide each side by '-8'. v = 4 Simplifying v = 4
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