How do solve #(x-2)/(x+4)<=0# and write the answer as a inequality and interval notation?

1 Answer
Nov 18, 2016

Answer:

Inequality notation: #x<=2#
Interval notation: #(-oo,2]#

Explanation:

#(x-2)/(x+4)<=0#

Multiply both sides by #x+4#

#(cancel((x+4))(x-2))/cancel((x+4))<=0(x+4)#

#x-2<=0#

Add #2# to both sides

#x<=2# (this answer is in inequality notation)

Interval notation:
The interval #x<=2# contains all the values that is less than or equal to #2# "from #(2)# to#(-oo)#", we can write this in interval notation by putting the bigger number #(2)# on the right and the smaller one#(-oo)# on the left:

#(-oo,2]#

We put the bracket #]# behind the #2# because #2# is included in the interval.