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Simplifying 5 + -1(1 + 6v) = 3v + 7(-4v + 6) 5 + (1 * -1 + 6v * -1) = 3v + 7(-4v + 6) 5 + (-1 + -6v) = 3v + 7(-4v + 6) Combine like terms: 5 + -1 = 4 4 + -6v = 3v + 7(-4v + 6) Reorder the terms: 4 + -6v = 3v + 7(6 + -4v) 4 + -6v = 3v + (6 * 7 + -4v * 7) 4 + -6v = 3v + (42 + -28v) Reorder the terms: 4 + -6v = 42 + 3v + -28v Combine like terms: 3v + -28v = -25v 4 + -6v = 42 + -25v Solving 4 + -6v = 42 + -25v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '25v' to each side of the equation. 4 + -6v + 25v = 42 + -25v + 25v Combine like terms: -6v + 25v = 19v 4 + 19v = 42 + -25v + 25v Combine like terms: -25v + 25v = 0 4 + 19v = 42 + 0 4 + 19v = 42 Add '-4' to each side of the equation. 4 + -4 + 19v = 42 + -4 Combine like terms: 4 + -4 = 0 0 + 19v = 42 + -4 19v = 42 + -4 Combine like terms: 42 + -4 = 38 19v = 38 Divide each side by '19'. v = 2 Simplifying v = 2
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