Home > Algebra > Multi-Step Inequalities

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

Answer 1

#-4 < x < 1#

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 #(x-1)(x+4) < 0#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Abramson

The solution to the inequality ( (x - 1)(x + 4) < 0 ) is ( 1 < x < -4 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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