Par Manufacturing manufactures steel rods. Suppose the rods ordered by a customer are manufactured to a specification of 0.5 in. and are acceptable only if they are within the tolerance limits of 0.49 in. and 0.51 in. Letting x denote the diameter of a rod, write an inequality using absolute value signs to express a criterion involving x that must be satisfied in order for a rod to be acceptable.
0.49<= X <= 0.51.
To write an inequality using absolute value signs to express the criterion for a rod to be acceptable, we need to consider the tolerance limits.
Let x be the diameter of a rod.
For the rod to be acceptable, it should satisfy the condition that its diameter is within the tolerance limits of 0.49 in. and 0.51 in.
Using absolute value, we can express this condition as:
| x - 0.5 | ≤ 0.01
Explanation:
- First, we take the difference between x and the target diameter of 0.5 in. This is represented as x - 0.5.
- Then, we take the absolute value of this difference to disregard the direction of the value.
- Finally, we state that the absolute value of the difference should be less than or equal to the tolerance limit of 0.01 in.
Therefore, the inequality using absolute value signs to express the criterion for a rod to be acceptable is | x - 0.5 | ≤ 0.01.