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Simplifying -5(3v + -6) + 7v = 4(v + 9) Reorder the terms: -5(-6 + 3v) + 7v = 4(v + 9) (-6 * -5 + 3v * -5) + 7v = 4(v + 9) (30 + -15v) + 7v = 4(v + 9) Combine like terms: -15v + 7v = -8v 30 + -8v = 4(v + 9) Reorder the terms: 30 + -8v = 4(9 + v) 30 + -8v = (9 * 4 + v * 4) 30 + -8v = (36 + 4v) Solving 30 + -8v = 36 + 4v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-4v' to each side of the equation. 30 + -8v + -4v = 36 + 4v + -4v Combine like terms: -8v + -4v = -12v 30 + -12v = 36 + 4v + -4v Combine like terms: 4v + -4v = 0 30 + -12v = 36 + 0 30 + -12v = 36 Add '-30' to each side of the equation. 30 + -30 + -12v = 36 + -30 Combine like terms: 30 + -30 = 0 0 + -12v = 36 + -30 -12v = 36 + -30 Combine like terms: 36 + -30 = 6 -12v = 6 Divide each side by '-12'. v = -0.5 Simplifying v = -0.5
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