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Simplifying 3(v + 2) + 2v = 7(v + -1) + 19 Reorder the terms: 3(2 + v) + 2v = 7(v + -1) + 19 (2 * 3 + v * 3) + 2v = 7(v + -1) + 19 (6 + 3v) + 2v = 7(v + -1) + 19 Combine like terms: 3v + 2v = 5v 6 + 5v = 7(v + -1) + 19 Reorder the terms: 6 + 5v = 7(-1 + v) + 19 6 + 5v = (-1 * 7 + v * 7) + 19 6 + 5v = (-7 + 7v) + 19 Reorder the terms: 6 + 5v = -7 + 19 + 7v Combine like terms: -7 + 19 = 12 6 + 5v = 12 + 7v Solving 6 + 5v = 12 + 7v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7v' to each side of the equation. 6 + 5v + -7v = 12 + 7v + -7v Combine like terms: 5v + -7v = -2v 6 + -2v = 12 + 7v + -7v Combine like terms: 7v + -7v = 0 6 + -2v = 12 + 0 6 + -2v = 12 Add '-6' to each side of the equation. 6 + -6 + -2v = 12 + -6 Combine like terms: 6 + -6 = 0 0 + -2v = 12 + -6 -2v = 12 + -6 Combine like terms: 12 + -6 = 6 -2v = 6 Divide each side by '-2'. v = -3 Simplifying v = -3
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