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

1 Answer
Aug 14, 2015

Answer:

#-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 :
enter image source here

#{: ("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 #(x-1)(x+4) < 0#