Chapter 3.3, Problem 40E

To determine

To find: the absolute value inequality for the given situation and the value of x.

Answer to Problem 40E

Absolute value of inequality: $\left|x-37.5\right|\le 1.2$

Possible values of x: $36.3\le x\le 38.7$

Explanation of Solution

Given information:

The actual quantity of unknown sample is x.

Quantity of unknown sample weighed is $37.5\pm 1.2\text{ grams}$

Calculation:

The absolute value of inequality will be as follows:

  $\left|x-37.5\right|\le 1.2$

The outcomes of the given equality can be either of the two shown below.

  $x-37.5\ge -1.2$..........(1)

  $x-37.5\le 1.2$..........(2)

Solve inequality (1) as follows:

  $\begin{array}{c}x-37.5\ge -1.2\\ x-37.5+37.5\ge -1.2+37.5\left[\text{Add 37}\text{.5 on both the sides}\right]\\ \therefore x\ge 36.3\end{array}$

Solve inequality (2) as follows:

  $\begin{array}{c}x-37.5\le 1.2\\ x-37.5+37.5\le 1.2+37.5\left[\text{Add 37}\text{.5 on both the sides}\right]\\ \therefore x\le 38.7\end{array}$

Thus, all the possible value of x for inequality is $36.3\le x\le 38.7$ .