Question

The specification for a length x is 43.6 cm with a tolerance of 0.1 cm. Write the specification as an absolute value inequality.

Answer 1

My answer to the problem is as follows:

Expressed as an absolute value. 

The difference between the actual length, x, and the specification, 43.6, can be no more than 0.1 

|x - 43.6| ≤ 0.1 <––––– 

The 43.6 is the target length, and the tolerance of 0.1 is how far off from the target is acceptable.

Answer 2

Answer:

$43.5\leq x\leq 43.7$

Step-by-step explanation:

We have been given that the specification for a length x is 43.6 cm with a tolerance of 0.1 cm. We are asked to write given specification as an absolute value.

$|\text{Actual-Ideal}|\leq \text{Tolerence}$

Upon substituting our given values, we will get:

$|x-43.6|\leq 0.1$

Using absolute value definition $|x|\leq a=-a\leq x\leq a$, we will get:

$-0.1\leq x-43.6\leq 0.1$

$-0.1+43.6\leq x-43.6+43.6 \leq 0.1+43.6$

$43.5\leq x \leq 43.7$

Therefore, our required inequality would be $43.5\leq x \leq 43.7$.