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Simplifying 71 = 5(3k + -8) + -2(3k + 2) Reorder the terms: 71 = 5(-8 + 3k) + -2(3k + 2) 71 = (-8 * 5 + 3k * 5) + -2(3k + 2) 71 = (-40 + 15k) + -2(3k + 2) Reorder the terms: 71 = -40 + 15k + -2(2 + 3k) 71 = -40 + 15k + (2 * -2 + 3k * -2) 71 = -40 + 15k + (-4 + -6k) Reorder the terms: 71 = -40 + -4 + 15k + -6k Combine like terms: -40 + -4 = -44 71 = -44 + 15k + -6k Combine like terms: 15k + -6k = 9k 71 = -44 + 9k Solving 71 = -44 + 9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9k' to each side of the equation. 71 + -9k = -44 + 9k + -9k Combine like terms: 9k + -9k = 0 71 + -9k = -44 + 0 71 + -9k = -44 Add '-71' to each side of the equation. 71 + -71 + -9k = -44 + -71 Combine like terms: 71 + -71 = 0 0 + -9k = -44 + -71 -9k = -44 + -71 Combine like terms: -44 + -71 = -115 -9k = -115 Divide each side by '-9'. k = 12.77777778 Simplifying k = 12.77777778
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