Theoretically, if you know the value of a, it's an easy problem. Let's say a=(-6).
|4x(-6) + 5| > 10?
Absolute value brackets act as parentheses. (no stuff)
|-24 + 5| = -19
-19 =/= 10
problem solved
Absolute value brackets do not act as parentheses.
|4x + 5| > 10
This is solved in two cases:
Case 1:
4x + 5 > 10
Case 2:
4x + 5 < -10
The answers to both of these equations are needed for the correct final answer.
Case 1:
4x + 5 > 10
Subtract 5 from both sides.
4x > 5
x > 1.25
Case 2:
4x + 5 < -10
Once again, subtract five from both sides.
4x < -15
x < -3.75
So the answer set is "x > 1.25 or x < -3.75".
Graphing this on a number line is my big problem. I have some understanding of how it works but in practice, I just fail miserably.
Blockland: That game where you solve absolute value inequalities