A certain rod in an internal combustion engine is supposed to be 5.9 inches. The tolerance on the rod is 0.0006 inches. If x represents the length of a rod, the acceptable lengths of a rod can be expressed as StartAbsoluteValue x minus 5.9 EndAbsoluteValue less than or equals 0.0006. Determine the acceptable lengths of the rod.

The acceptable lengths of the rod are the lengths between 5.8994 and 5.9006 inches.

Step-by-step explanation:

If the acceptable lengths of a rod can be expressed as:

| x - 5.9 | ≤ 0.0006

Now, if we have that:

| a | ≤ b

it can be written as:

-b ≤ a ≤ b

Then, the acceptable lengths of a rod can be also expressed as:

-0.0006 ≤ x - 5.9 ≤ 0.0006

So, if we sum 5.9 at every part of the inequation, we get:

-0.0006 + 5.9 ≤ x ≤ 0.0006 + 5.9

5.8994 ≤ x ≤ 5.9006

It means the acceptable lengths of the rod are the lengths between 5.8994 and 5.9006 inches.