expr in shell programming

i am new to shell programming, currently using redhat linux of version
2.4.20-8.
i have problem in executing expr command in the following shell script

$ x=5
$ x='expr $x + 1'
$ echo $x

the output is displaying always
expr $x + 1

Pls guide me for the above query

Use

`expr $x + 1`

use the symbol on that is on "~" on your key board

I prefer to avoid "expr":

x=5
((x+=1))
echo $x