# How do you solve the inequality: (x - 1) (x + 4) < 0?

Aug 14, 2015

$- 4 < x < 1$

#### Explanation:

Note that the left side of this inequality would be equal to $0$
if $x = - 4$ or $x = 1$

We could divide the number line up into 3 ranges :

{: ("Range",color(white)("XXX"),(x-1), color(white)("XXX"),(x+4),color(white)("XXX"),"product"), ("A",color(white)("XXX"),< 0, color(white)("XXX"),< 0,color(white)("XXX"),<0), ("B",color(white)("XXX"),< 0,color(white)("XXX"),> 0,color(white)("XXX"),< 0), ("C",color(white)("XXX"),> 0, color(white)("XXX"),> 0, color(white)("XXX"),> 0) :}

Only in Range "B" is the product $\left(x - 1\right) \left(x + 4\right) < 0$