Question

write an absolute value inequality for the graph below. use x for your variable. the inequality is \boxed{}. \boxed{<}\boxed{} \boxed{>}\boxed{} \boxed{\leq}\boxed{}

Explanation:

Step1: Find the midpoint (h)

The two endpoints are -5 and 5. The midpoint \( h \) is calculated as \( \frac{-5 + 5}{2} = 0 \).

Step2: Find the distance (k) from midpoint to endpoint

The distance from 0 to 5 (or -5) is \( |5 - 0| = 5 \).

Step3: Write the absolute value inequality

The general form for an absolute value inequality representing a segment between \( h - k \) and \( h + k \) with inclusive endpoints is \( |x - h| \leq k \). Substituting \( h = 0 \) and \( k = 5 \), we get \( |x - 0| \leq 5 \), which simplifies to \( |x| \leq 5 \).

Answer:

\(|x| \leq 5\)