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! :)

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- Mar 4th 2013, 10:14 PMSimimanoStraight 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 PMEducatedRe: 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 PMSimimanoRe: 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 PMEducatedRe: 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:

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