-2

In fact, we have to solve 2 inequalities simultaneously:

5x-3>-2  (1)

5x-3<12  (2)

Let's solve the first inequality:

5x-3>-2 

We'll add both sides the value 2. Because it's a positive value, the inequality remains unchanged.

5x-3+2>-2+2

5x-1>0

Let's add now the value 1, keeping unchanged the inequality:

5x>1

We'll divide by 5, both sides:

x>1/5 so x belongs to the interval (1/5 , +inf.)

Now, let's solve the second inequality:

5x-3<12

First, we'll move the the value -3, to the right side, by changing it's sign:

5x<12+3

5x<15

Now, we'll divide by 5:

x<3, so x belongs to the interval (-inf. , 3).

The common solution is the intersection of both intervals and we'll get the interval (1/5 , 3).