Question

point b lies between points a and c on \\( \overline { a c } \\). let x represent the length of segment ab in inches
use the segment to complete the statements
the value of x is
the length of \\( \overline { a b } \\) in inches is
the length of \\( \overline { a c } \\) in inches is
20 inches

Explanation:

Step1: Set up the equation

Since \( AB + BC=AC \), and \( AB = x \), \( BC = 3x \), \( AC=20 \), we have the equation \( x + 3x=20 \).

Step2: Simplify the left - hand side

Combine like terms: \( 4x = 20 \).

Step3: Solve for \( x \)

Divide both sides by \( 4 \): \( x=\frac{20}{4}=5 \).

Step4: Find the length of \( \overline{AB} \)

Since \( AB=x \), then \( AB = 5 \) inches.

Step5: Recall the length of \( \overline{AC} \)

Given \( AC = 20 \) inches.

Answer:

The value of \( x \) is \( 5 \).
The length of \( \overline{AB} \) in inches is \( 5 \).
The length of \( \overline{AC} \) in inches is \( 20 \).