what is the absolute value of 21- I 2x-4 I=13?

Answer 1

Do you mean solve for x?

21 - | 2x - 4 | = 13

Subtract 21 from both sides to get the absolute value alone:
- | 2x - 4 | = 13 - 21
- | 2x - 4 | = -8

Multiply both sides by -1 to remove the negative signs:
| 2x - 4 | = 8

Now you can rewrite this as two equations:
2x - 4 = 8
2x - 4 = -8

Solve them separately:
2x - 4 = 8
2x = 12
x = 6

2x - 4 = -8
2x = -8 + 4
2x = -4
x = -2

Your two solutions are:
x = 6 or x = -2