Question

1. (triangle with markings: two equal segments on one side, two equal segments on the other side, a midline labeled 5x + 3, and the base labeled 9x + 15)

Explanation:

Step1: Identify Midsegment Theorem

The segment \(5x + 3\) is a midsegment of the triangle (since it connects midpoints of two sides, as indicated by the marks). By the Midsegment Theorem, the midsegment is half the length of the third side. So, \(5x + 3=\frac{1}{2}(9x + 15)\).

Step2: Solve the Equation

Multiply both sides by 2: \(2(5x + 3)=9x + 15\)
Simplify left side: \(10x + 6 = 9x + 15\)
Subtract \(9x\) from both sides: \(x + 6 = 15\)
Subtract 6: \(x = 9\)

Answer:

\(x = 9\)