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Simplifying 7(5 + -1v) = 8(v + -5) (5 * 7 + -1v * 7) = 8(v + -5) (35 + -7v) = 8(v + -5) Reorder the terms: 35 + -7v = 8(-5 + v) 35 + -7v = (-5 * 8 + v * 8) 35 + -7v = (-40 + 8v) Solving 35 + -7v = -40 + 8v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-8v' to each side of the equation. 35 + -7v + -8v = -40 + 8v + -8v Combine like terms: -7v + -8v = -15v 35 + -15v = -40 + 8v + -8v Combine like terms: 8v + -8v = 0 35 + -15v = -40 + 0 35 + -15v = -40 Add '-35' to each side of the equation. 35 + -35 + -15v = -40 + -35 Combine like terms: 35 + -35 = 0 0 + -15v = -40 + -35 -15v = -40 + -35 Combine like terms: -40 + -35 = -75 -15v = -75 Divide each side by '-15'. v = 5 Simplifying v = 5
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