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Simplifying 7v + -5 + 2(3v + 6) = -5(v + 1) Reorder the terms: 7v + -5 + 2(6 + 3v) = -5(v + 1) 7v + -5 + (6 * 2 + 3v * 2) = -5(v + 1) 7v + -5 + (12 + 6v) = -5(v + 1) Reorder the terms: -5 + 12 + 7v + 6v = -5(v + 1) Combine like terms: -5 + 12 = 7 7 + 7v + 6v = -5(v + 1) Combine like terms: 7v + 6v = 13v 7 + 13v = -5(v + 1) Reorder the terms: 7 + 13v = -5(1 + v) 7 + 13v = (1 * -5 + v * -5) 7 + 13v = (-5 + -5v) Solving 7 + 13v = -5 + -5v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5v' to each side of the equation. 7 + 13v + 5v = -5 + -5v + 5v Combine like terms: 13v + 5v = 18v 7 + 18v = -5 + -5v + 5v Combine like terms: -5v + 5v = 0 7 + 18v = -5 + 0 7 + 18v = -5 Add '-7' to each side of the equation. 7 + -7 + 18v = -5 + -7 Combine like terms: 7 + -7 = 0 0 + 18v = -5 + -7 18v = -5 + -7 Combine like terms: -5 + -7 = -12 18v = -12 Divide each side by '18'. v = -0.6666666667 Simplifying v = -0.6666666667
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