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Simplifying -7(v + 4) + 3v + 5 = 8v + 7 Reorder the terms: -7(4 + v) + 3v + 5 = 8v + 7 (4 * -7 + v * -7) + 3v + 5 = 8v + 7 (-28 + -7v) + 3v + 5 = 8v + 7 Reorder the terms: -28 + 5 + -7v + 3v = 8v + 7 Combine like terms: -28 + 5 = -23 -23 + -7v + 3v = 8v + 7 Combine like terms: -7v + 3v = -4v -23 + -4v = 8v + 7 Reorder the terms: -23 + -4v = 7 + 8v Solving -23 + -4v = 7 + 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. -23 + -4v + -8v = 7 + 8v + -8v Combine like terms: -4v + -8v = -12v -23 + -12v = 7 + 8v + -8v Combine like terms: 8v + -8v = 0 -23 + -12v = 7 + 0 -23 + -12v = 7 Add '23' to each side of the equation. -23 + 23 + -12v = 7 + 23 Combine like terms: -23 + 23 = 0 0 + -12v = 7 + 23 -12v = 7 + 23 Combine like terms: 7 + 23 = 30 -12v = 30 Divide each side by '-12'. v = -2.5 Simplifying v = -2.5
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