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Simplifying 7(6 + -38v) + 27(11 + 13v) = -1 (6 * 7 + -38v * 7) + 27(11 + 13v) = -1 (42 + -266v) + 27(11 + 13v) = -1 42 + -266v + (11 * 27 + 13v * 27) = -1 42 + -266v + (297 + 351v) = -1 Reorder the terms: 42 + 297 + -266v + 351v = -1 Combine like terms: 42 + 297 = 339 339 + -266v + 351v = -1 Combine like terms: -266v + 351v = 85v 339 + 85v = -1 Solving 339 + 85v = -1 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-339' to each side of the equation. 339 + -339 + 85v = -1 + -339 Combine like terms: 339 + -339 = 0 0 + 85v = -1 + -339 85v = -1 + -339 Combine like terms: -1 + -339 = -340 85v = -340 Divide each side by '85'. v = -4 Simplifying v = -4
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