Question

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

Answer 1

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.