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Simplifying 13(v + -6) = 5v + 2(5v + 12) Reorder the terms: 13(-6 + v) = 5v + 2(5v + 12) (-6 * 13 + v * 13) = 5v + 2(5v + 12) (-78 + 13v) = 5v + 2(5v + 12) Reorder the terms: -78 + 13v = 5v + 2(12 + 5v) -78 + 13v = 5v + (12 * 2 + 5v * 2) -78 + 13v = 5v + (24 + 10v) Reorder the terms: -78 + 13v = 24 + 5v + 10v Combine like terms: 5v + 10v = 15v -78 + 13v = 24 + 15v Solving -78 + 13v = 24 + 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. -78 + 13v + -15v = 24 + 15v + -15v Combine like terms: 13v + -15v = -2v -78 + -2v = 24 + 15v + -15v Combine like terms: 15v + -15v = 0 -78 + -2v = 24 + 0 -78 + -2v = 24 Add '78' to each side of the equation. -78 + 78 + -2v = 24 + 78 Combine like terms: -78 + 78 = 0 0 + -2v = 24 + 78 -2v = 24 + 78 Combine like terms: 24 + 78 = 102 -2v = 102 Divide each side by '-2'. v = -51 Simplifying v = -51
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