Straight forward inequality question

• Mar 4th 2013, 10:14 PM
Simimano
Straight forward inequality question
Hi guys..

I would like a simple explanation as of to how to get the solution set of an inequality;

4x+5 < 5x-9

Thanks! :)
• Mar 4th 2013, 10:26 PM
Educated
Re: Straight forward inequality question
Move all the x's to one side. Move all the numbers to the other side.

Eg.

$4x+5 < 5x-9$

$5 + 9 < 5x - 4x$

$14 < x$

(Just note that in inequalities when you divide or multiply by a negavive number you have to switch the direction of the inequality)
• Mar 4th 2013, 10:42 PM
Simimano
Re: Straight forward inequality question
Thanks, that inequality solution set is quite straight forward..But when I hit this one in the text book..I was a bit confused, could you perhaps shed some light on it:

-2 ≦ x+1≦3

Thanks a lot!!
• Mar 4th 2013, 10:55 PM
Educated
Re: Straight forward inequality question
It's pretty much the same thing, just recall basic algebra:

$x-2 = y$

To get the 2 to the other side, we add 2 to both sides:

$x-2 +2 = y +2$

$x = y +2$

It's the exact same thing here with this inequality:

$-2 \le x + 1 \le 3$

Subtract 1 from all parts:

$-2 -1 \le x + 1 -1 \le 3-1$

So we get:

$-3 \le x\le 2$