# How do you solve 2x-5<x+1?

May 11, 2015

You can solve it as a normal equation isolating $x$ on one side (changing signs when necessary) and "reading", at the end, the result:
$2 x - x < 5 + 1$
$x < 6$
This tells you that for the first equation to be smaller than the second you cal only choose values of $x$ which are $< 6$.
If you try, for example, $x = 7$ (which is bigger than $6$) you get:
$2 \cdot 7 - 5 < 7 + 1$
$9 < 8$ which is not true!
Instead if you try, for example, $x = 5$ (which is smaller than $6$) you get:
$2 \cdot 5 - 5 < 5 + 1$
$5 < 6$ which is true!

Hope it helps!