Question

writing an inequality in exercises 117 and 118, write an absolute value inequality that represents the interval. 117.

number line with 0, 1, 2, 3, 4, 5, 6; open circles at 1 and 5, line segment between them

Explanation:

Step1: Find the midpoint of the interval

The interval is from \(1\) to \(5\). The midpoint \(a\) is calculated as \(\frac{1 + 5}{2}=\frac{6}{2} = 3\).

Step2: Find the distance from midpoint to endpoints

The distance \(b\) from the midpoint \(3\) to either endpoint (\(1\) or \(5\)) is \(|3 - 1|=2\) (or \(|5 - 3| = 2\)).

Step3: Write the absolute value inequality

The general form of an absolute value inequality representing an interval \((a - b,a + b)\) is \(|x - a|If \(|x - 3|<2\), then \(- 2

Answer:

\(|x - 3| < 2\)