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Simplifying 15(v + -1) + 4(v + 3) = 2(7 + v) Reorder the terms: 15(-1 + v) + 4(v + 3) = 2(7 + v) (-1 * 15 + v * 15) + 4(v + 3) = 2(7 + v) (-15 + 15v) + 4(v + 3) = 2(7 + v) Reorder the terms: -15 + 15v + 4(3 + v) = 2(7 + v) -15 + 15v + (3 * 4 + v * 4) = 2(7 + v) -15 + 15v + (12 + 4v) = 2(7 + v) Reorder the terms: -15 + 12 + 15v + 4v = 2(7 + v) Combine like terms: -15 + 12 = -3 -3 + 15v + 4v = 2(7 + v) Combine like terms: 15v + 4v = 19v -3 + 19v = 2(7 + v) -3 + 19v = (7 * 2 + v * 2) -3 + 19v = (14 + 2v) Solving -3 + 19v = 14 + 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. -3 + 19v + -2v = 14 + 2v + -2v Combine like terms: 19v + -2v = 17v -3 + 17v = 14 + 2v + -2v Combine like terms: 2v + -2v = 0 -3 + 17v = 14 + 0 -3 + 17v = 14 Add '3' to each side of the equation. -3 + 3 + 17v = 14 + 3 Combine like terms: -3 + 3 = 0 0 + 17v = 14 + 3 17v = 14 + 3 Combine like terms: 14 + 3 = 17 17v = 17 Divide each side by '17'. v = 1 Simplifying v = 1
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