I am able to solve regular inequalities but not this type
2x+1 < 5x-8
Approach inequalities like a regular equation. The only thing you Must keep in mind is to flip the sign whenever you divide by a negative number.
Here's an example:
$\displaystyle -1-5x < -3x + 7$
$\displaystyle -2x < 8$
divide both sides by -2, therefore sign flips.
$\displaystyle x > -4$
Hope it helped.
Because you have not taken the correct steps.
$\displaystyle 2x+1<5x-8$
Add 8 to both sides, the left is still less than the right
since 3<7, therefore 3+8<7+8 for example.
$\displaystyle 2x+1+8<5x+8-8$
$\displaystyle 2x+9<5x$
$\displaystyle 5x>2x+9$
Now subtract 2x from both sides.
This gets you to what is probably quite familiar to you.