||x - 4|- 3| + 4 < |2x + 5|

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- January 1st 2007, 05:25 PM #1

- January 1st 2007, 06:08 PM #2

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Again, you need to consider to cases for absolute for one non-negative and one negative. That is the standard way of doing these nasty ones.

for non-negative value.

for negative value.

for non-negative value.

For negative value.

Now we divide the problem into cases,

thus,

thus,

thus,

thus. .

And you do what I did before.

In each of these cases the absolute sign disappearsn and you deal with a different inequality. If the set of contradicts the condition from the intersection.