# If |3x – 7| > 2, then x

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. $x<\frac{5}{3}$