In order ton solve the given inequality, the first thing we have to do is to get rid of the "| |" by applying the solution of the absolute value function, like this:
|2x - 15| < 7
Then;
-7 < 2x - 15 < 7
Now, let's solve for x from each one of the expressions we got, like this:
• For -7 < 2x - 15
-7 + 15 < 2x
8 < 2x
8/2 < x
4 < x
x > 4
• For 2x - 15 < 7
2x < 7 + 15
2x < 22
x < 22/2
x < 11
Then, x < 11 and x > 4 is the solution for the given inequality