Question

1. line l bisects line segment uw. find the value of a.

Explanation:

Step1: Set up equation

Since line \(l\) bisects line - segment \(UW\), then \(UV = VW\). So we set up the equation \(3a + 5=6a - 7\).

Step2: Isolate variable terms

Subtract \(3a\) from both sides of the equation: \(3a+5 - 3a=6a - 7-3a\), which simplifies to \(5 = 3a-7\).

Step3: Solve for \(a\)

Add 7 to both sides: \(5 + 7=3a-7 + 7\), getting \(12 = 3a\). Then divide both sides by 3: \(\frac{12}{3}=\frac{3a}{3}\), so \(a = 4\).

Answer:

\(a = 4\)