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Simplifying 7(v + 1) + -4(5 + -2v) = -5(v + -9) Reorder the terms: 7(1 + v) + -4(5 + -2v) = -5(v + -9) (1 * 7 + v * 7) + -4(5 + -2v) = -5(v + -9) (7 + 7v) + -4(5 + -2v) = -5(v + -9) 7 + 7v + (5 * -4 + -2v * -4) = -5(v + -9) 7 + 7v + (-20 + 8v) = -5(v + -9) Reorder the terms: 7 + -20 + 7v + 8v = -5(v + -9) Combine like terms: 7 + -20 = -13 -13 + 7v + 8v = -5(v + -9) Combine like terms: 7v + 8v = 15v -13 + 15v = -5(v + -9) Reorder the terms: -13 + 15v = -5(-9 + v) -13 + 15v = (-9 * -5 + v * -5) -13 + 15v = (45 + -5v) Solving -13 + 15v = 45 + -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. -13 + 15v + 5v = 45 + -5v + 5v Combine like terms: 15v + 5v = 20v -13 + 20v = 45 + -5v + 5v Combine like terms: -5v + 5v = 0 -13 + 20v = 45 + 0 -13 + 20v = 45 Add '13' to each side of the equation. -13 + 13 + 20v = 45 + 13 Combine like terms: -13 + 13 = 0 0 + 20v = 45 + 13 20v = 45 + 13 Combine like terms: 45 + 13 = 58 20v = 58 Divide each side by '20'. v = 2.9 Simplifying v = 2.9
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