Find the value of a, if:

 Modulus(2a-3)=3a+2

Modulus(2a-3) = 3a+2, which can also be written as |2a-3| = 3a+2.

Modulus function  f(x) = |x| is defined as

|x| = x, for x>0,

|x| = -x, for x<0

So, we get two cases here,

Case (1):

2a-3>0

$$\Rightarrow a>\frac{3}{2}$$........................(1)

|2a-3| = 2a-3 = 3a+2

$$\Rightarrow a = -5$$

But from equation (1), The above value of a = -5 is not a possible case.

Case (2):

2a-3<0

$$\Rightarrow a<\frac{3}{2}$$....................(2)

|2a-3| = -(2a-3) = 3a+2

$$\Rightarrow a = \frac{1}{5}$$

This is a possible case, hence the value of $$a = \frac{1}{5}$$