Question

What are the solution intervals for |2x – 1| + 6 > 9?

Answer 1

First subtract 6 from both sides

Answer 2

We end up with
\[\left| 2x -1 \right| > 3\]

Answer 3

First step for any absolute value question is to isolate the | | part.

Answer 4

Now is the tricky part

Answer 5

Since its an absolute value if what ever is in the bars is >3 it work, but if what ever is in the bars is less than -3 it also works!

Answer 6

so we then split it up into two inequalities

Answer 7

Either:
2x-1 is greater than 3

Or:
2x-1 is less than -3

Answer 8

\[2x-1 > 3 \space \text{and} \space 2x-1 < -3 \]

Answer 9

We then solve those regularly

Answer 10

Absolute values inequalities are like mirrors, when you take any number's absolute value, it turns out to be positive, that's why you can split that in half, once you take the absolute valute, it becomes something like this:

Solution can be either positive or negative, due to the power of | | s.