Question

draw and label a picture for each question if b is between a and c. then find x and ab.

1. ( ab = 2x ), ( bc = 5x + 4 ), and ( ac = 32 )
2. ( ab = 4x ), ( overline{ab} cong overline{bc} ), and ( ac = 24 )

Explanation:

Step1: Use the segment - addition postulate

Since \(B\) is between \(A\) and \(C\), by the segment - addition postulate \(AB + BC=AC\).
Given \(AB = 2x\), \(BC = 5x + 4\), and \(AC = 32\), we substitute these values into the equation:
\(2x+(5x + 4)=32\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+5x+4 = 32\), which gives \(7x+4 = 32\)

Step3: Solve for \(x\)

Subtract \(4\) from both sides of the equation: \(7x+4 - 4=32 - 4\), so \(7x=28\)
Divide both sides by \(7\): \(x=\frac{28}{7}=4\)

Step4: Find \(AB\)

Since \(AB = 2x\) and \(x = 4\), then \(AB=2\times4 = 8\)

Answer:

\(x = 4\) and \(AB = 8\)