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Simplifying 2[k + -1(4k + -13) + 9] = 2(k + 4) Reorder the terms: 2[k + -1(-13 + 4k) + 9] = 2(k + 4) 2[k + (-13 * -1 + 4k * -1) + 9] = 2(k + 4) 2[k + (13 + -4k) + 9] = 2(k + 4) Reorder the terms: 2[13 + 9 + k + -4k] = 2(k + 4) Combine like terms: 13 + 9 = 22 2[22 + k + -4k] = 2(k + 4) Combine like terms: k + -4k = -3k 2[22 + -3k] = 2(k + 4) [22 * 2 + -3k * 2] = 2(k + 4) [44 + -6k] = 2(k + 4) Reorder the terms: 44 + -6k = 2(4 + k) 44 + -6k = (4 * 2 + k * 2) 44 + -6k = (8 + 2k) Solving 44 + -6k = 8 + 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. 44 + -6k + -2k = 8 + 2k + -2k Combine like terms: -6k + -2k = -8k 44 + -8k = 8 + 2k + -2k Combine like terms: 2k + -2k = 0 44 + -8k = 8 + 0 44 + -8k = 8 Add '-44' to each side of the equation. 44 + -44 + -8k = 8 + -44 Combine like terms: 44 + -44 = 0 0 + -8k = 8 + -44 -8k = 8 + -44 Combine like terms: 8 + -44 = -36 -8k = -36 Divide each side by '-8'. k = 4.5 Simplifying k = 4.5
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