Question

write an absolute value equation that represents the graph shown. your answer should use the form |x - a| = b or |x + a| = b, where a and b are whole numbers, decimals, or simplified fractions.

Explanation:

Step1: Find the midpoint (a)

The two points on the number line are 7 and 13. The midpoint \( a \) is calculated as the average of these two points.

$$ a=\frac{7 + 13}{2}=\frac{20}{2}=10 $$

Step2: Find the distance (b) from the midpoint to either point

The distance \( b \) from the midpoint \( a = 10 \) to either 7 or 13. Let's take 13:

$$ b=\vert13 - 10\vert= 3 $$

Or taking 7:

$$ b=\vert7 - 10\vert=\vert- 3\vert = 3 $$

The absolute value equation in the form \(|x - a|=b\) with \( a = 10 \) and \( b = 3 \) is \(|x - 10|=3\).

Answer:

\(|x - 10| = 3\)