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Simplifying 1 + -9v + 6 + 6v = -7(v + 11) + -12(v + 7) Reorder the terms: 1 + 6 + -9v + 6v = -7(v + 11) + -12(v + 7) Combine like terms: 1 + 6 = 7 7 + -9v + 6v = -7(v + 11) + -12(v + 7) Combine like terms: -9v + 6v = -3v 7 + -3v = -7(v + 11) + -12(v + 7) Reorder the terms: 7 + -3v = -7(11 + v) + -12(v + 7) 7 + -3v = (11 * -7 + v * -7) + -12(v + 7) 7 + -3v = (-77 + -7v) + -12(v + 7) Reorder the terms: 7 + -3v = -77 + -7v + -12(7 + v) 7 + -3v = -77 + -7v + (7 * -12 + v * -12) 7 + -3v = -77 + -7v + (-84 + -12v) Reorder the terms: 7 + -3v = -77 + -84 + -7v + -12v Combine like terms: -77 + -84 = -161 7 + -3v = -161 + -7v + -12v Combine like terms: -7v + -12v = -19v 7 + -3v = -161 + -19v Solving 7 + -3v = -161 + -19v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '19v' to each side of the equation. 7 + -3v + 19v = -161 + -19v + 19v Combine like terms: -3v + 19v = 16v 7 + 16v = -161 + -19v + 19v Combine like terms: -19v + 19v = 0 7 + 16v = -161 + 0 7 + 16v = -161 Add '-7' to each side of the equation. 7 + -7 + 16v = -161 + -7 Combine like terms: 7 + -7 = 0 0 + 16v = -161 + -7 16v = -161 + -7 Combine like terms: -161 + -7 = -168 16v = -168 Divide each side by '16'. v = -10.5 Simplifying v = -10.5
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