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Simplifying 5(1 + v) + 2 = 8(v + -4) (1 * 5 + v * 5) + 2 = 8(v + -4) (5 + 5v) + 2 = 8(v + -4) Reorder the terms: 5 + 2 + 5v = 8(v + -4) Combine like terms: 5 + 2 = 7 7 + 5v = 8(v + -4) Reorder the terms: 7 + 5v = 8(-4 + v) 7 + 5v = (-4 * 8 + v * 8) 7 + 5v = (-32 + 8v) Solving 7 + 5v = -32 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. 7 + 5v + -8v = -32 + 8v + -8v Combine like terms: 5v + -8v = -3v 7 + -3v = -32 + 8v + -8v Combine like terms: 8v + -8v = 0 7 + -3v = -32 + 0 7 + -3v = -32 Add '-7' to each side of the equation. 7 + -7 + -3v = -32 + -7 Combine like terms: 7 + -7 = 0 0 + -3v = -32 + -7 -3v = -32 + -7 Combine like terms: -32 + -7 = -39 -3v = -39 Divide each side by '-3'. v = 13 Simplifying v = 13
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