Question

Write and solve an absolute inequality to represent this situation.

Answer 1

A)

`1.5\leq x\leq5`

B) Yes, he has to add more chlorine.

Explanation:

What is being said, in other words, is that the absolute difference between the chlorine levels of a sample x and 3.25 ppm has to be, at most, 1.75 ppm.

This situation can be described by the absolute value inequality:

`\lvert{x-3.25}\rvert\leq1.75`

We can solve this inequality as following:

`\begin{gathered} \lvert x-3.25\rvert\leq1.75 \\ \rightarrow-1.75\leq x-3.25\leq1.75 \\ \\ \Rightarrow1.5\leq x\leq5 \end{gathered}`

Now, notice that the sample exctracted by the lifeguard is below this interval. Therefore, we has to add more chlorine.