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Simplifying 7(2v + 1) + -3(9v + 2) = 40 Reorder the terms: 7(1 + 2v) + -3(9v + 2) = 40 (1 * 7 + 2v * 7) + -3(9v + 2) = 40 (7 + 14v) + -3(9v + 2) = 40 Reorder the terms: 7 + 14v + -3(2 + 9v) = 40 7 + 14v + (2 * -3 + 9v * -3) = 40 7 + 14v + (-6 + -27v) = 40 Reorder the terms: 7 + -6 + 14v + -27v = 40 Combine like terms: 7 + -6 = 1 1 + 14v + -27v = 40 Combine like terms: 14v + -27v = -13v 1 + -13v = 40 Solving 1 + -13v = 40 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -13v = 40 + -1 Combine like terms: 1 + -1 = 0 0 + -13v = 40 + -1 -13v = 40 + -1 Combine like terms: 40 + -1 = 39 -13v = 39 Divide each side by '-13'. v = -3 Simplifying v = -3
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