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Simplifying 4k + -5(k + -8) = 2(k + 2) Reorder the terms: 4k + -5(-8 + k) = 2(k + 2) 4k + (-8 * -5 + k * -5) = 2(k + 2) 4k + (40 + -5k) = 2(k + 2) Reorder the terms: 40 + 4k + -5k = 2(k + 2) Combine like terms: 4k + -5k = -1k 40 + -1k = 2(k + 2) Reorder the terms: 40 + -1k = 2(2 + k) 40 + -1k = (2 * 2 + k * 2) 40 + -1k = (4 + 2k) Solving 40 + -1k = 4 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 40 + -1k + -2k = 4 + 2k + -2k Combine like terms: -1k + -2k = -3k 40 + -3k = 4 + 2k + -2k Combine like terms: 2k + -2k = 0 40 + -3k = 4 + 0 40 + -3k = 4 Add '-40' to each side of the equation. 40 + -40 + -3k = 4 + -40 Combine like terms: 40 + -40 = 0 0 + -3k = 4 + -40 -3k = 4 + -40 Combine like terms: 4 + -40 = -36 -3k = -36 Divide each side by '-3'. k = 12 Simplifying k = 12
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