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Simplifying 9(-5 + v) = 12v + -6(v + 7) (-5 * 9 + v * 9) = 12v + -6(v + 7) (-45 + 9v) = 12v + -6(v + 7) Reorder the terms: -45 + 9v = 12v + -6(7 + v) -45 + 9v = 12v + (7 * -6 + v * -6) -45 + 9v = 12v + (-42 + -6v) Reorder the terms: -45 + 9v = -42 + 12v + -6v Combine like terms: 12v + -6v = 6v -45 + 9v = -42 + 6v Solving -45 + 9v = -42 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. -45 + 9v + -6v = -42 + 6v + -6v Combine like terms: 9v + -6v = 3v -45 + 3v = -42 + 6v + -6v Combine like terms: 6v + -6v = 0 -45 + 3v = -42 + 0 -45 + 3v = -42 Add '45' to each side of the equation. -45 + 45 + 3v = -42 + 45 Combine like terms: -45 + 45 = 0 0 + 3v = -42 + 45 3v = -42 + 45 Combine like terms: -42 + 45 = 3 3v = 3 Divide each side by '3'. v = 1 Simplifying v = 1
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