Determine the value of k such that the inequality $4x – k(x + 3) ≥ 12 – 4(2 + x)$ has no real solutions, where k is a constant.

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Official Explanation

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Starting with the inequality

4x – k(x + 3) ≥ 12 – 4(2 + x)

, we can simplify it to

4x - kx - 3k ≥ 12 - 8 - 4x

. This leads to

(8 - k)x ≥ 4 + 3k

.…

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What this question tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.