Dear experts, please solve the following inequality
➩ mod(2 ÷ x - 4) is greater than 1, x is not equal to 4.

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Given}, \\ \left|\frac{2}{\mathrm{x}-4}\right|>1 \\ \frac{2}{\mathrm{x}-4}>1 \\ 2>\mathrm{x}-4 \\ \mathrm{x}<6 \\ \mathrm{or} \\ \frac{2}{\mathrm{x}-4}<-1 \\ \mathrm{x}-4>-2 \\ \mathrm{x}>2 \\ \mathrm{hence} \mathrm{we} \mathrm{get} , \\ \mathrm{x}>2 \\ \mathrm{x}<6 \\ \mathrm{and} \mathrm{x} \mathrm{not} \mathrm{equal} \mathrm{to} 4 \\ \mathrm{so} \mathrm{ans} \mathrm{is} \mathrm{x}\in \left(2,4\right)\cup \left(4,6\right) \mathrm{here} 2 \mathrm{and} 6 \mathrm{are} \mathrm{included}. \end{gathered}$$

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