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Simplifying 7(v + 6) = -4(3v + -9) + 5v Reorder the terms: 7(6 + v) = -4(3v + -9) + 5v (6 * 7 + v * 7) = -4(3v + -9) + 5v (42 + 7v) = -4(3v + -9) + 5v Reorder the terms: 42 + 7v = -4(-9 + 3v) + 5v 42 + 7v = (-9 * -4 + 3v * -4) + 5v 42 + 7v = (36 + -12v) + 5v Combine like terms: -12v + 5v = -7v 42 + 7v = 36 + -7v Solving 42 + 7v = 36 + -7v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '7v' to each side of the equation. 42 + 7v + 7v = 36 + -7v + 7v Combine like terms: 7v + 7v = 14v 42 + 14v = 36 + -7v + 7v Combine like terms: -7v + 7v = 0 42 + 14v = 36 + 0 42 + 14v = 36 Add '-42' to each side of the equation. 42 + -42 + 14v = 36 + -42 Combine like terms: 42 + -42 = 0 0 + 14v = 36 + -42 14v = 36 + -42 Combine like terms: 36 + -42 = -6 14v = -6 Divide each side by '14'. v = -0.4285714286 Simplifying v = -0.4285714286
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