Like Denis, I also wonder where you're stuck and how much you already know. Posting an exercise with no work shown, and no questions asked about specific steps, makes it hard to know where to start helping.
To remove the absolute value symbols from inequalities, we use the following rules.
If the inequality symbol is "greater than", then we're working with something that looks like
|expression| > constant
Because of the absolute value symbols, this statement actually means two different inequalities:
expression > constant
expression < -constant
If the given inequality symbol is "less than", then we've got
|expression| < constant
This statement also means two inequalities.
expression < constant
expression > -constant
We can write these last two as a compound inequality:
-constant < expression < constant
Here's two examples to show these rules using values.
|7x - 3| > 40
Remove the absolute value symbols as explained above, and write two new inequalities.
7x - 3 > 40
7x - 3 < -40
|22t + 5| < 9
Remove the absolute value symbols as explained above for |expression|<constant.
-9 < 22t + 5 < 9
The given inequality in your exercise is not ready to apply the rule because |2r-3| is not by itself on one side of the inequality symbol.
Carry out the two operations needed to get |2r - 3| by itself on the left-hand side, and then apply the rule to get rid of the absolute value symbols.
Solve the two resulting inequalities, and go from there.
Please show whatever work you can accomplish, if you would like more help with this exercise. Try to say something about WHY you're stuck, so that I might determine where to continue helping.
By the way, if you understand the perception of absolute value as a distance from zero on the Real number line, and you realize that there are two possible directions to move away from zero on the Real number line, then these rules are easy to remember.
|x| > 10
This statement tells us that valid numbers for x are all located more than 10 units away from zero on the Real number line. But we can move away from zero toward positive 10 or we can move away from zero toward -10. In order for a value to be more than 10 units away from zero in either direction, it must be more than 10 or less than -10.
x > 10
x < -10
Likewise, |x| < 10 tells us that valid numbers for x are within 10 units distance from zero. They cannot be 10 or more units to the right of zero, and they cannot be 10 or more units to the left of zero. They are inbetween.
-10 < x < 10
This is the same as writing the union of the following two sets.
x < 10
x > -10