How do you solve compound Inequality 2x < 10 and -5x < 5?

Jul 11, 2015

There are two rules working here

Explanation:

(1)
You may divide both sides by a positive number without problems:
$2 x < 10 \to x < 5$

(2)
If you divide (or multiply by a negative number, the direction of the inequatlity sign changes:
$- 5 x < 5 \to$ (divide by -5) $x > - 1 \to - 1 < x$

We can combine these:
$- 1 < x < 5$