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Simplifying -2[4(5 + 2) + -3(k + 1)] = 14 + 2k Combine like terms: 5 + 2 = 7 -2[4(7) + -3(k + 1)] = 14 + 2k Multiply 4 * 7 -2[28 + -3(k + 1)] = 14 + 2k Reorder the terms: -2[28 + -3(1 + k)] = 14 + 2k -2[28 + (1 * -3 + k * -3)] = 14 + 2k -2[28 + (-3 + -3k)] = 14 + 2k Combine like terms: 28 + -3 = 25 -2[25 + -3k] = 14 + 2k [25 * -2 + -3k * -2] = 14 + 2k [-50 + 6k] = 14 + 2k Solving -50 + 6k = 14 + 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. -50 + 6k + -2k = 14 + 2k + -2k Combine like terms: 6k + -2k = 4k -50 + 4k = 14 + 2k + -2k Combine like terms: 2k + -2k = 0 -50 + 4k = 14 + 0 -50 + 4k = 14 Add '50' to each side of the equation. -50 + 50 + 4k = 14 + 50 Combine like terms: -50 + 50 = 0 0 + 4k = 14 + 50 4k = 14 + 50 Combine like terms: 14 + 50 = 64 4k = 64 Divide each side by '4'. k = 16 Simplifying k = 16
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