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Simplifying -12v + -8(-1v + -8) = -2 + 3(v + 1) Reorder the terms: -12v + -8(-8 + -1v) = -2 + 3(v + 1) -12v + (-8 * -8 + -1v * -8) = -2 + 3(v + 1) -12v + (64 + 8v) = -2 + 3(v + 1) Reorder the terms: 64 + -12v + 8v = -2 + 3(v + 1) Combine like terms: -12v + 8v = -4v 64 + -4v = -2 + 3(v + 1) Reorder the terms: 64 + -4v = -2 + 3(1 + v) 64 + -4v = -2 + (1 * 3 + v * 3) 64 + -4v = -2 + (3 + 3v) Combine like terms: -2 + 3 = 1 64 + -4v = 1 + 3v Solving 64 + -4v = 1 + 3v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3v' to each side of the equation. 64 + -4v + -3v = 1 + 3v + -3v Combine like terms: -4v + -3v = -7v 64 + -7v = 1 + 3v + -3v Combine like terms: 3v + -3v = 0 64 + -7v = 1 + 0 64 + -7v = 1 Add '-64' to each side of the equation. 64 + -64 + -7v = 1 + -64 Combine like terms: 64 + -64 = 0 0 + -7v = 1 + -64 -7v = 1 + -64 Combine like terms: 1 + -64 = -63 -7v = -63 Divide each side by '-7'. v = 9 Simplifying v = 9
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