Example 1 from Algebra and Trigonometry, 3.6 Absolute Value Functions

Using Absolute Value to Determine Resistance

Electrical parts, such as resistors and capacitors, come with specified values of their operating parameters: resistance, capacitance, etc. However, due to imprecision in manufacturing, the actual values of these parameters vary somewhat from piece to piece, even when they are supposed to be the same. The best that manufacturers can do is to try to guarantee that the variations will stay within a specified range, often $±1%, \pm 5%,$ or $\pm 10% .$

Suppose we have a resistor rated at 680 ohms, $\pm 5 % .$ Use the absolute value function to express the range of possible values of the actual resistance.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We can find that 5% of 680 ohms is 34 ohms. The absolute value of the difference between the actual and nominal resistance should not exceed the stated variability, so, with the resistance $R$ in ohms,
$| R - 680 | \leq 34$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Students who score within 20 points of 80 will pass a test. Write this as a distance from 80 using absolute value notation.

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Solution

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Solution

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