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Simplifying 19 = -3(8 + -7v) + -1(4v + 8) 19 = (8 * -3 + -7v * -3) + -1(4v + 8) 19 = (-24 + 21v) + -1(4v + 8) Reorder the terms: 19 = -24 + 21v + -1(8 + 4v) 19 = -24 + 21v + (8 * -1 + 4v * -1) 19 = -24 + 21v + (-8 + -4v) Reorder the terms: 19 = -24 + -8 + 21v + -4v Combine like terms: -24 + -8 = -32 19 = -32 + 21v + -4v Combine like terms: 21v + -4v = 17v 19 = -32 + 17v Solving 19 = -32 + 17v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-17v' to each side of the equation. 19 + -17v = -32 + 17v + -17v Combine like terms: 17v + -17v = 0 19 + -17v = -32 + 0 19 + -17v = -32 Add '-19' to each side of the equation. 19 + -19 + -17v = -32 + -19 Combine like terms: 19 + -19 = 0 0 + -17v = -32 + -19 -17v = -32 + -19 Combine like terms: -32 + -19 = -51 -17v = -51 Divide each side by '-17'. v = 3 Simplifying v = 3
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