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Simplifying 11(k + -2) + 2[k + -3(k + 1)] = 0 Reorder the terms: 11(-2 + k) + 2[k + -3(k + 1)] = 0 (-2 * 11 + k * 11) + 2[k + -3(k + 1)] = 0 (-22 + 11k) + 2[k + -3(k + 1)] = 0 Reorder the terms: -22 + 11k + 2[k + -3(1 + k)] = 0 -22 + 11k + 2[k + (1 * -3 + k * -3)] = 0 -22 + 11k + 2[k + (-3 + -3k)] = 0 Reorder the terms: -22 + 11k + 2[-3 + k + -3k] = 0 Combine like terms: k + -3k = -2k -22 + 11k + 2[-3 + -2k] = 0 -22 + 11k + [-3 * 2 + -2k * 2] = 0 -22 + 11k + [-6 + -4k] = 0 Reorder the terms: -22 + -6 + 11k + -4k = 0 Combine like terms: -22 + -6 = -28 -28 + 11k + -4k = 0 Combine like terms: 11k + -4k = 7k -28 + 7k = 0 Solving -28 + 7k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + 7k = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 7k = 0 + 28 7k = 0 + 28 Combine like terms: 0 + 28 = 28 7k = 28 Divide each side by '7'. k = 4 Simplifying k = 4
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