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Find the solutions of the inequality
|2x-5|>x+1.
First we consider the case where
,
i.e.
.
In this case
|2x-5|=2x-5, so we can write the inequality as
2x-5>x+1.
Subtracting x on both sides and adding 5, we get
x>6.
Now consider the case 2x-5< 0, i.e.
.
In this case
|2x-5|=-(2x-5)=5-2x, so we can write the inequality as
5-2x>x+1.
Adding 2x and subtracting 1 on both sides yields
4>3x,
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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Helmut Knaust
1998-06-08
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