The epic gamers who made my lesson didnt even gloss over this

When you have absolute values, that esentially shows how far from zero the number is. This goes both ways — the absolute value of 5 and -5 is the same, as both of them are 5 “places” away from 0.

When solving anything with absolute values, you must do separate “cases”. In this case you have 2 of those — when the expression in the absolute brackets is negative, and when its positive.

First, lets say its positive. The absolute value is 2x - 3, and if its positive it just stays the original way (2x - 3) and you solve it normally:

|2x - 3| - 4 <= 5
2x - 3 - 4 <= 5
2x <= 5 + 3 + 4
2x <= 12
x <= 6

Then we have when its negative, where you put a minus in front of the expression under the brackets:

-(2x - 3) - 4 <= 5
-2x + 3 - 4 <= 5
-2x - 1 <= 5
-2x <= 6 (multiply by -1, and the inequality sign changes)
2x => -6
x => -3

So your x would be -3 <= x <= 6.

What are the following algebraic equations. you need to post those if you want the answer