Answer:
[tex]21.78\leq x\leq 22.22[/tex]
Step-by-step explanation:
Let x represent the actual length of pipe.
We have been given that Robert is inspecting a shipment of 22-inch pipes. The lengths of the pipes may vary by 1%.
To find the range of allowable lengths of the pipes, we will use tolerance calculation formula.
[tex]|\text{Atual}-\text{Ideal}|\leq \text{Tolerance}[/tex]
The variation in the lengths of pipes is 1% of ideal length that is 22.
[tex]22\times \frac{1}{100}=0.22[/tex]
Upon substituting, our given values, we will get:
[tex]|x-22|\leq 0.22[/tex]
Use absolute value rule: If [tex]|u|\leq a[/tex], then [tex]-a\leq u\leq a[/tex]
[tex]-0.22\leq x-22\leq 0.22[/tex]
Adding 22 on all sides:
[tex]-0.22+22\leq x-22+22\leq 0.22+22[/tex]
[tex]21.78\leq x\leq 22.22[/tex]
Therefore, the range of allowable lengths of the pipes is [tex]21.78\leq x\leq 22.22[/tex].
