Chapter 1.7, Problem 120E

Thickness of a Laminate A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.020 in., with a tolerance of 0.003 in.

1. (a) Find an inequality involving absolute values that describes the range of possible thickness for the laminate.
2. (b) Solve the inequality you found in part (a).

To determine

The absolute value inequality for the thickness of laminate.

Answer to Problem 120E

The absolute value inequality for the thickness of the laminate is $\underset{\_}{\left|t-0.020\right|\le 0.003}$.

Explanation of Solution

The thickness of the industrial laminates is 0.020 in and the tolerance of the laminate is 0.003 in.

Let the thickness of the laminating sheet be t.

The difference between the thickness x and specified thickness 0.020 is less than the tolerance of the laminate 0.003.

The above can be written as absolute value of inequality as follows:

$\begin{array}{l}-0.003\le t-0.020\le 0.003\\ \left|t-0.020\right|\le 0.003\end{array}$

Therefore, the absolute value inequality for the thickness of the laminate is $\underset{\_}{\left|t-0.020\right|\le 0.003}$.

To determine

The solution of the inequality in part (a).

Answer to Problem 120E

The solution of the inequality is $\underset{\_}{0.017\le t\le 0.023}$.

Explanation of Solution

From part (a), $\left|t-0.020\right|\le 0.003$.

Solve $\left|t-0.020\right|\le 0.003$ as follows:

$\begin{array}{l}\left|t-0.020\right|\le 0.003\\ -0.003\le t-0.020\le 0.003\\ -0.003+0.020\le t-0.020+0.020\le 0.003+0.02\\ 0.017\le t\le 0.023\end{array}$

Thus, the solution of the inequality is $\underset{\_}{0.017\le t\le 0.023}$.