10-14 Absolute value

To evaluate a number inside absolute value bars, such as | -4 |,
If what's inside the bars is positive, you take away the bars and the sign stays positive.
If what's inside the bars is negative, you take away the bars and the sign is changed to positive.
In this case, what's inside the bars is negative, so you change it to positive 4 when you remove the bars.

| -4 | = 4

If you don't know the sign of what's inside the bars because there's a variable (letter) you don't know,
You have to consider the two cases where what's inside could be positive and what's inside could be negative, depending on the value of the variable.

| x | = x, positive x, if x is positive
| x | = -x, the opposite of x, if x is negative

| x + 3 | = x + 3, if x  > -3
| x + 3 | = -x - 3, the opposite, if x < -3

This means that when you are solving absolute value equations or inequalities, once you remove the bars you will have to work on two parts of the problem.  The final answer will be the joining or junction of two graphs.  It could be two dots, two split arrows, or the overlapping tails of two arrows.