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!
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)
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:
$\displaystyle -3 \le x\le 2$