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Simplifying 40 = 5(9v + 2) + -4(7v + 1) Reorder the terms: 40 = 5(2 + 9v) + -4(7v + 1) 40 = (2 * 5 + 9v * 5) + -4(7v + 1) 40 = (10 + 45v) + -4(7v + 1) Reorder the terms: 40 = 10 + 45v + -4(1 + 7v) 40 = 10 + 45v + (1 * -4 + 7v * -4) 40 = 10 + 45v + (-4 + -28v) Reorder the terms: 40 = 10 + -4 + 45v + -28v Combine like terms: 10 + -4 = 6 40 = 6 + 45v + -28v Combine like terms: 45v + -28v = 17v 40 = 6 + 17v Solving 40 = 6 + 17v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-17v' to each side of the equation. 40 + -17v = 6 + 17v + -17v Combine like terms: 17v + -17v = 0 40 + -17v = 6 + 0 40 + -17v = 6 Add '-40' to each side of the equation. 40 + -40 + -17v = 6 + -40 Combine like terms: 40 + -40 = 0 0 + -17v = 6 + -40 -17v = 6 + -40 Combine like terms: 6 + -40 = -34 -17v = -34 Divide each side by '-17'. v = 2 Simplifying v = 2
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