Question

1. 6x + 24, 4x - 1 (with a triangle diagram showing midline and congruent markings)

Explanation:

Step1: Identify Midline Theorem

The segment \(4x - 1\) is a midline of the triangle (since it connects midpoints, as indicated by congruent marks on sides), so it's half the length of the base \(6x + 24\). Thus, \(4x - 1=\frac{1}{2}(6x + 24)\).

Step2: Solve the Equation

Multiply both sides by 2: \(2(4x - 1)=6x + 24\)
Simplify: \(8x - 2 = 6x + 24\)
Subtract \(6x\) and add 2: \(8x - 6x=24 + 2\)
Simplify: \(2x = 26\)
Divide by 2: \(x = 13\)

Answer:

\(x = 13\)