Advertisements
Advertisements
Question
\[\frac{3}{x - 2} < 1\]
Advertisements
Solution
\[\frac{3}{x - 2} < 1\]
\[ \Rightarrow \frac{3}{x - 2} - 1 < 0\]
\[ \Rightarrow \frac{3 - x + 2}{x - 2} < 0\]
\[ \Rightarrow \frac{- x + 5}{x - 2} < 0\]
\[ \Rightarrow \frac{x - 5}{x - 2} > 0\]
\[ \Rightarrow \frac{3}{x - 2} - 1 < 0\]
\[ \Rightarrow \frac{3 - x + 2}{x - 2} < 0\]
\[ \Rightarrow \frac{- x + 5}{x - 2} < 0\]
\[ \Rightarrow \frac{x - 5}{x - 2} > 0\]
∴ \[x \in \left( - \infty , 2 \right) \cup \left( 5, \infty \right)\]
shaalaa.com
Is there an error in this question or solution?
