Chapter ISG, Problem 3.8.13P

To determine

To Find: The absolute value equation to determine the maximum and minimum diameters of bolts to pass the inspection.

Answer to Problem 3.8.13P

  $|x-6.5|=0.04$

Maximum diameter = 6.54 mm

Minimum diameter = 6.46 mm

Explanation of Solution

Given:

Tolerance of 0.04 mm. Diameter of bolt = 6.5 mm

Given that there can be a tolerance of 0.04 mm in the actual bolt produced from the expected diameter of the bolt.

Let the actual diameter of the bolt be $x$ mm.

The absolute value equation can be written as:

  $|x-6.5|=0.04$

As per definition of absolute value function:

  $\left|x\right|=\{\begin{array}{c}x,x>0\\ -x,x<0\end{array}$

Here, diameter of the bolt can be more than the expected diameter. i.e. $x-6.5>0$

As per definition, solving the absolute value equation with positive sign:

  $x-6.5=0.04\Rightarrow x=6.54$

Or, weight of bag can be lesser than the labeled weight. i.e. $x-6.5<0$

As per definition, solving the absolute value equation with positive sign:

  $-(x-6.5)=0.04\Rightarrow x=6.46$

Therefore, to pass the inspection:

Maximum diameter = 6.54 mm

Minimum diameter = 6.46 mm