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Simplifying 7(v + -3) + -1(4v + -2) = 8v + 4 + -5 Reorder the terms: 7(-3 + v) + -1(4v + -2) = 8v + 4 + -5 (-3 * 7 + v * 7) + -1(4v + -2) = 8v + 4 + -5 (-21 + 7v) + -1(4v + -2) = 8v + 4 + -5 Reorder the terms: -21 + 7v + -1(-2 + 4v) = 8v + 4 + -5 -21 + 7v + (-2 * -1 + 4v * -1) = 8v + 4 + -5 -21 + 7v + (2 + -4v) = 8v + 4 + -5 Reorder the terms: -21 + 2 + 7v + -4v = 8v + 4 + -5 Combine like terms: -21 + 2 = -19 -19 + 7v + -4v = 8v + 4 + -5 Combine like terms: 7v + -4v = 3v -19 + 3v = 8v + 4 + -5 Reorder the terms: -19 + 3v = 4 + -5 + 8v Combine like terms: 4 + -5 = -1 -19 + 3v = -1 + 8v Solving -19 + 3v = -1 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. -19 + 3v + -8v = -1 + 8v + -8v Combine like terms: 3v + -8v = -5v -19 + -5v = -1 + 8v + -8v Combine like terms: 8v + -8v = 0 -19 + -5v = -1 + 0 -19 + -5v = -1 Add '19' to each side of the equation. -19 + 19 + -5v = -1 + 19 Combine like terms: -19 + 19 = 0 0 + -5v = -1 + 19 -5v = -1 + 19 Combine like terms: -1 + 19 = 18 -5v = 18 Divide each side by '-5'. v = -3.6 Simplifying v = -3.6
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