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Simplifying 7 = 3(v + 3) + -8(v + 4) Reorder the terms: 7 = 3(3 + v) + -8(v + 4) 7 = (3 * 3 + v * 3) + -8(v + 4) 7 = (9 + 3v) + -8(v + 4) Reorder the terms: 7 = 9 + 3v + -8(4 + v) 7 = 9 + 3v + (4 * -8 + v * -8) 7 = 9 + 3v + (-32 + -8v) Reorder the terms: 7 = 9 + -32 + 3v + -8v Combine like terms: 9 + -32 = -23 7 = -23 + 3v + -8v Combine like terms: 3v + -8v = -5v 7 = -23 + -5v Solving 7 = -23 + -5v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5v' to each side of the equation. 7 + 5v = -23 + -5v + 5v Combine like terms: -5v + 5v = 0 7 + 5v = -23 + 0 7 + 5v = -23 Add '-7' to each side of the equation. 7 + -7 + 5v = -23 + -7 Combine like terms: 7 + -7 = 0 0 + 5v = -23 + -7 5v = -23 + -7 Combine like terms: -23 + -7 = -30 5v = -30 Divide each side by '5'. v = -6 Simplifying v = -6
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