What is the solution to this inequality: $|2x+5| <\frac{1}{2}$

Question

I am using this method but my answer is coming wrong. Where am I wrong?

Answer 1

You want $2x+5\lt\frac12$ and $2x+5\gt -\frac12$...

Answer 2

Note that by definition $|z| $ is equal to $z $ if $z>0$; and equal to $-z $ if $z\leq 0$.

So if we want to solve $|z|<a$ ($a $ non-negative number) we need to have:

For $z>0$, $z $ must be less than $a $;

and for $z <0$, $-z $ must be less than $a $, or equivalently $z>-a $.

Hence $-a <z <a$.

In your case $-\frac {1}{2}<2x+5 <\frac {1}{2}$. Now solve for $x $.