Question

2x + 35, 5x - 22, line segment with points a, m, b (a---|----m----|----b)

Explanation:

Step1: Set the two expressions equal (midpoint)

Since \( m \) is the midpoint of segment \( AB \), the lengths \( 2x + 35 \) and \( 5x - 22 \) are equal. So we set up the equation:
\( 2x + 35 = 5x - 22 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\( 35 = 3x - 22 \)
Add 22 to both sides:
\( 35 + 22 = 3x \)
\( 57 = 3x \)
Divide both sides by 3:
\( x = \frac{57}{3} = 19 \)

Step3: Find the length of each segment (optional, but to verify)

First segment: \( 2x + 35 = 2(19) + 35 = 38 + 35 = 73 \)
Second segment: \( 5x - 22 = 5(19) - 22 = 95 - 22 = 73 \) (verifies they are equal)

Answer:

\( x = 19 \)