Let l be the acceptable length and w be the acceptable width of the rectangles. First we can find the acceptable range for the length and then we do the same way for the width.
Length
Since the rectangle's length must be within 0.05 in of the desired size, the absolute value of the difference between 18.55 and l should be less than 0.05. We can write this as the following absolute valueinequality.
|l-18.55|<0.05
Since any negative argument inside the absolute value changes signs to be positive, we get a compound inequality when removing the absolute value. Because the difference needs to be less than 0.05 away from the absolute value, we get an and compound inequality.
- 0.05
Let's split the compound inequality into two separate ones.
Compound inequality:&& - 0.05
Width
Similarly, as the rectangle's width must also be within 0.05 in of the desired size, we get the following inequality.
|w-36.75|<0.05
Since any negative argument inside the absolute value changes signs to be positive, we get a compound inequality when removing the absolute value. Because the difference needs to be less than 0.05 away from the absolute value, we get an and compound inequality.
- 0.05
