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Simplifying -7(v + 4) + 2v + 6 = 8v + 12 Reorder the terms: -7(4 + v) + 2v + 6 = 8v + 12 (4 * -7 + v * -7) + 2v + 6 = 8v + 12 (-28 + -7v) + 2v + 6 = 8v + 12 Reorder the terms: -28 + 6 + -7v + 2v = 8v + 12 Combine like terms: -28 + 6 = -22 -22 + -7v + 2v = 8v + 12 Combine like terms: -7v + 2v = -5v -22 + -5v = 8v + 12 Reorder the terms: -22 + -5v = 12 + 8v Solving -22 + -5v = 12 + 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. -22 + -5v + -8v = 12 + 8v + -8v Combine like terms: -5v + -8v = -13v -22 + -13v = 12 + 8v + -8v Combine like terms: 8v + -8v = 0 -22 + -13v = 12 + 0 -22 + -13v = 12 Add '22' to each side of the equation. -22 + 22 + -13v = 12 + 22 Combine like terms: -22 + 22 = 0 0 + -13v = 12 + 22 -13v = 12 + 22 Combine like terms: 12 + 22 = 34 -13v = 34 Divide each side by '-13'. v = -2.615384615 Simplifying v = -2.615384615
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