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Simplifying v + -7 + 4(3v + 2) = -2(v + 1) Reorder the terms: v + -7 + 4(2 + 3v) = -2(v + 1) v + -7 + (2 * 4 + 3v * 4) = -2(v + 1) v + -7 + (8 + 12v) = -2(v + 1) Reorder the terms: -7 + 8 + v + 12v = -2(v + 1) Combine like terms: -7 + 8 = 1 1 + v + 12v = -2(v + 1) Combine like terms: v + 12v = 13v 1 + 13v = -2(v + 1) Reorder the terms: 1 + 13v = -2(1 + v) 1 + 13v = (1 * -2 + v * -2) 1 + 13v = (-2 + -2v) Solving 1 + 13v = -2 + -2v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2v' to each side of the equation. 1 + 13v + 2v = -2 + -2v + 2v Combine like terms: 13v + 2v = 15v 1 + 15v = -2 + -2v + 2v Combine like terms: -2v + 2v = 0 1 + 15v = -2 + 0 1 + 15v = -2 Add '-1' to each side of the equation. 1 + -1 + 15v = -2 + -1 Combine like terms: 1 + -1 = 0 0 + 15v = -2 + -1 15v = -2 + -1 Combine like terms: -2 + -1 = -3 15v = -3 Divide each side by '15'. v = -0.2 Simplifying v = -0.2
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