How do you solve the compound inequalities 60 < 20u < 120?

Jul 15, 2018

$u \in \left(3 , 6\right)$

Explanation:

$\text{divide all intervals by 20}$

$3 < u < 6 \text{ is the solution}$

$u \in \left(3 , 6\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$

Jul 15, 2018

$3 < u < 6$

Interval notation: $\left(3 , 6\right)$

Explanation:

Remember, the end goal is to isolate $u$. To go about doing this, we can divide all intervals by $20$. We get

$3 < u < 6$

This means the solutions of this inequality are values of $u$ between $3$ and $6$, not including those.

We can alternatively write this in interval notation as

$\left(3 , 6\right)$

Notice that we used parenthesis as opposed to brackets when we don't include the end values.

Hope this helps!