Inequalities and absolute values

[mcgarryseanm]

When solving an inequality with an absolute value, do you automatically flip the sign of the second inequality?

ex.

|2x-4| > 4

2x -4 > 4 AND 2x - 4 < -4

I think this is correct?

So

2x > 8 2x < 0

x > 4 x < 0

[tommywallach]

Yep! Well done.

You can also think of it as just putting a negative sign in front of the absolute value thing.

|2x-4| > 4

2x - 4 > 4

AND

-2x + 4 > 4

It amounts to the same thing.

-t