Math CentralQuandaries & Queries


Question from Alena:

I'm trying to help with a homework problem. Can you please help me?

2kx - 3k < 2x + 4 +3kx

We are solving for "k" with no solution.

Hi Alena,

I would start by adding -(2kx - 3k) to each side and then adding -(2x + 4) to each side to obtain

\[-(2x + 4) < kx + 3k\]


\[-(2x + 4) < k(x + 3).\]

If you are solving for $k$ then you could divide each side by $x + 3$ keeping in mind that is $x + 3 > 0$ then the direction of the inequality remains unchanged and is $x + 3 < 0$ then the direction of the inequality is reversed. But you are looking for the case where there is no solution. What value of $x$ gives no solution?


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