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

1 Answer
Nov 18, 2016

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.