# 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;

Please explain using this example:

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.

\$\displaystyle 4x+5 < 5x-9\$

\$\displaystyle 5 + 9 < 5x - 4x\$

\$\displaystyle 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:

\$\displaystyle x-2 = y \$

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

\$\displaystyle x-2 +2 = y +2\$

\$\displaystyle x = y +2\$

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

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

Subtract 1 from all parts:

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

So we get:

\$\displaystyle -3 \le x\le 2\$