Learn the four ways to eliminate absolute value bars:

1.          is equivalent to this:  "  "

2.          is equivalent to this:  "  " 

3.          is equivalent to this: "         "

4.          is equivalent to this: "         "

Yours is case 1:

   |6x-5| < 10 is equivalent to

     -10 < 6x-5 < 10

We solve for x in the middle:

Add +5 to all three sides like this:

     -10 < 6x-5 < 10
      +5     +5   +5
      -5 < 6x   < 15

Dow divide all three sides by 6

       < x  < 

The fraction on the right reduces to 

       < x  < 

In interval notation that is:

         
   


Edwin