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Exercises Functions

Example 1 from Precalculus, 1.6 Absolute Value Functions

Determine a Number within a Prescribed Distance

Describe all values $x$ within or including a distance of 4 from the number 5.

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 want the distance between $x$ and 5 to be less than or equal to 4. We can draw a number line, such as the one in Figure 2, to represent the condition to be satisfied.

Figure 2

The distance from $x$ to 5 can be represented using the absolute value as $| x - 5 | .$ We want the values of $x$ that satisfy the condition $| x - 5 | \leq 4.$

Your turn

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

Describe all values $x$ within a distance of 3 from the number 2.

How did it go?

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From Precalculus (1st edition) by OpenStax (Rice University), section 1.6, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.