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Simplifying 9(k + -4) + -1(2 + k) = 2k Reorder the terms: 9(-4 + k) + -1(2 + k) = 2k (-4 * 9 + k * 9) + -1(2 + k) = 2k (-36 + 9k) + -1(2 + k) = 2k -36 + 9k + (2 * -1 + k * -1) = 2k -36 + 9k + (-2 + -1k) = 2k Reorder the terms: -36 + -2 + 9k + -1k = 2k Combine like terms: -36 + -2 = -38 -38 + 9k + -1k = 2k Combine like terms: 9k + -1k = 8k -38 + 8k = 2k Solving -38 + 8k = 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. -38 + 8k + -2k = 2k + -2k Combine like terms: 8k + -2k = 6k -38 + 6k = 2k + -2k Combine like terms: 2k + -2k = 0 -38 + 6k = 0 Add '38' to each side of the equation. -38 + 38 + 6k = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 6k = 0 + 38 6k = 0 + 38 Combine like terms: 0 + 38 = 38 6k = 38 Divide each side by '6'. k = 6.333333333 Simplifying k = 6.333333333
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