|2*x*-5|>*x*+1.

First we consider the case where
,
i.e.
.
In this case
|2*x*-5|=2*x*-5, so we can write the inequality as

2*x*-5>*x*+1.

Subtracting

Now consider the case 2*x*-5< 0, i.e.
.
In this case
|2*x*-5|=-(2*x*-5)=5-2*x*, so we can write the inequality as

5-2*x*>*x*+1.

Adding 2

4>3*x*,

so we obtain the requirement that .

So a real number *x* is a solution of the original inequality if

or if

Thus the set of solutions is

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