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Simplifying 5(1 + -1v) + -5(2 + -1v) = 7v + -35 + 8v (1 * 5 + -1v * 5) + -5(2 + -1v) = 7v + -35 + 8v (5 + -5v) + -5(2 + -1v) = 7v + -35 + 8v 5 + -5v + (2 * -5 + -1v * -5) = 7v + -35 + 8v 5 + -5v + (-10 + 5v) = 7v + -35 + 8v Reorder the terms: 5 + -10 + -5v + 5v = 7v + -35 + 8v Combine like terms: 5 + -10 = -5 -5 + -5v + 5v = 7v + -35 + 8v Combine like terms: -5v + 5v = 0 -5 + 0 = 7v + -35 + 8v -5 = 7v + -35 + 8v Reorder the terms: -5 = -35 + 7v + 8v Combine like terms: 7v + 8v = 15v -5 = -35 + 15v Solving -5 = -35 + 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. -5 + -15v = -35 + 15v + -15v Combine like terms: 15v + -15v = 0 -5 + -15v = -35 + 0 -5 + -15v = -35 Add '5' to each side of the equation. -5 + 5 + -15v = -35 + 5 Combine like terms: -5 + 5 = 0 0 + -15v = -35 + 5 -15v = -35 + 5 Combine like terms: -35 + 5 = -30 -15v = -30 Divide each side by '-15'. v = 2 Simplifying v = 2
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