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1 X − 1 ≤ 2 - Mathematics

\[\frac{1}{x - 1} \leq 2\]

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Solution

\[\frac{1}{x - 1} \leq 2\]
\[ \Rightarrow \frac{1}{x - 1} - 2 \leq 0\]
\[ \Rightarrow \frac{1 - 2x + 2}{x - 1} \leq 0\]
\[ \Rightarrow \frac{- 2x + 3}{x - 1} \leq 0\]
\[ \Rightarrow \frac{2x - 3}{x - 1} \geq 0\]

∴ \[x \in \left( - \infty , 1 \right) \cup [\frac{3}{2}, \infty )\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.1 | Q 22 | Page 10
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