Question:
If $|3 x-7|>2$, then $x$ _______________$\frac{5}{3}$ or, $x$ __________________$3 .$
Solution:
|3x – 7| > 2
By defination of modulus inequality;
3x – 7 > 2 or 3x – 7 < –2
If 3x – 7 > 2
By adding 7 to both sides,
We get,
3x > 9
i.e. x > 9
If 3x – 7 < – 2
Now, by adding 7 to both sides,
We get,
$3 x-7+7<-2+7$
i.e. 3x < 5
i.e. $x<\frac{5}{3}$
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