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Simplifying 7(v + -1) = 3v + 5 + -3(-4v + -2) Reorder the terms: 7(-1 + v) = 3v + 5 + -3(-4v + -2) (-1 * 7 + v * 7) = 3v + 5 + -3(-4v + -2) (-7 + 7v) = 3v + 5 + -3(-4v + -2) Reorder the terms: -7 + 7v = 3v + 5 + -3(-2 + -4v) -7 + 7v = 3v + 5 + (-2 * -3 + -4v * -3) -7 + 7v = 3v + 5 + (6 + 12v) Reorder the terms: -7 + 7v = 5 + 6 + 3v + 12v Combine like terms: 5 + 6 = 11 -7 + 7v = 11 + 3v + 12v Combine like terms: 3v + 12v = 15v -7 + 7v = 11 + 15v Solving -7 + 7v = 11 + 15v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-15v' to each side of the equation. -7 + 7v + -15v = 11 + 15v + -15v Combine like terms: 7v + -15v = -8v -7 + -8v = 11 + 15v + -15v Combine like terms: 15v + -15v = 0 -7 + -8v = 11 + 0 -7 + -8v = 11 Add '7' to each side of the equation. -7 + 7 + -8v = 11 + 7 Combine like terms: -7 + 7 = 0 0 + -8v = 11 + 7 -8v = 11 + 7 Combine like terms: 11 + 7 = 18 -8v = 18 Divide each side by '-8'. v = -2.25 Simplifying v = -2.25
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