Question

line segment ef with midpoint m (marked by a dot). the segment from e to the first tick mark is labeled (7x - 40), and the segment from the second tick mark to f is labeled (3x - 20). the tick marks are symmetric around m (indicating m is the midpoint).

Explanation:

Assuming \( m \) is the midpoint of segment \( EF \), so the two segments \( E \) to \( m \) and \( m \) to \( F \) are equal. Thus, we set up the equation:

Step1: Set the two expressions equal

Since \( m \) is the midpoint, \( 7x - 40 = 3x - 20 \)

Step2: Subtract \( 3x \) from both sides

\( 7x - 3x - 40 = 3x - 3x - 20 \)
\( 4x - 40 = -20 \)

Step3: Add 40 to both sides

\( 4x - 40 + 40 = -20 + 40 \)
\( 4x = 20 \)

Step4: Divide both sides by 4

\( \frac{4x}{4} = \frac{20}{4} \)
\( x = 5 \)

Answer:

\( x = 5 \)