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Simplifying 5k + 2[-4(k + 3) + -1k] = 4 + -1(2k + 3) Reorder the terms: 5k + 2[-4(3 + k) + -1k] = 4 + -1(2k + 3) 5k + 2[(3 * -4 + k * -4) + -1k] = 4 + -1(2k + 3) 5k + 2[(-12 + -4k) + -1k] = 4 + -1(2k + 3) Combine like terms: -4k + -1k = -5k 5k + 2[-12 + -5k] = 4 + -1(2k + 3) 5k + [-12 * 2 + -5k * 2] = 4 + -1(2k + 3) 5k + [-24 + -10k] = 4 + -1(2k + 3) Reorder the terms: -24 + 5k + -10k = 4 + -1(2k + 3) Combine like terms: 5k + -10k = -5k -24 + -5k = 4 + -1(2k + 3) Reorder the terms: -24 + -5k = 4 + -1(3 + 2k) -24 + -5k = 4 + (3 * -1 + 2k * -1) -24 + -5k = 4 + (-3 + -2k) Combine like terms: 4 + -3 = 1 -24 + -5k = 1 + -2k Solving -24 + -5k = 1 + -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. -24 + -5k + 2k = 1 + -2k + 2k Combine like terms: -5k + 2k = -3k -24 + -3k = 1 + -2k + 2k Combine like terms: -2k + 2k = 0 -24 + -3k = 1 + 0 -24 + -3k = 1 Add '24' to each side of the equation. -24 + 24 + -3k = 1 + 24 Combine like terms: -24 + 24 = 0 0 + -3k = 1 + 24 -3k = 1 + 24 Combine like terms: 1 + 24 = 25 -3k = 25 Divide each side by '-3'. k = -8.333333333 Simplifying k = -8.333333333
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