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

Nov 18, 2016

Inequality notation: $x \le 2$
Interval notation: $\left(- \infty , 2\right]$

Explanation:

$\frac{x - 2}{x + 4} \le 0$

Multiply both sides by $x + 4$

$\frac{\cancel{\left(x + 4\right)} \left(x - 2\right)}{\cancel{\left(x + 4\right)}} \le 0 \left(x + 4\right)$

$x - 2 \le 0$

Add $2$ to both sides

$x \le 2$ (this answer is in inequality notation)

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

$\left(- \infty , 2\right]$

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