Chapter 7.1, Problem 64PPE

To determine

To find: The inequality for the acceptable range of diameters of metal rods.

Answer to Problem 64PPE

The inequality for the acceptable range of diameters of metal rods is $1.499\text{mm}<x<1.501\text{mm}$ .

Explanation of Solution

Given information:

The target diameter for the metal rods is $1.5\text{mm}$ , range of diameter at which rod is acceptable within is ${10}^{-3}$ of $1.5\text{mm}$ .

Calculation:

Let, the diameter of the metal rod be $x$ .

The range of diameter at which rod is acceptable within is:

  ${10}^{-3}$ of $1.5\text{mm}$

The given range ${10}^{-3}$ in fraction and decimal form is:

  $\begin{array}{c}{10}^{-3}=\frac{1}{{10}^3}\\ =\frac{1}{1000}\\ =0.001\end{array}$

The word ‘within’ implies that the acceptable range of diameters may not be greater than $1.50+0.001\text{mm}$ or less than $1.50-0.001\text{mm}$ . Thus, the acceptable range for the diameters of the rods is between $1.499\text{mm}$ and $1.501\text{mm}$ .The inequality will use the symbols of greater than or less than.

Therefore, the range for single inequality for acceptable range of diameters is $1.499\text{mm}<x<1.501\text{mm}$ .