Question

the length of $overline{df}$ is $(4x + 2)$ inches, with $e$ as the midpoint. the length of $overline{de}$ is 17 inches. what is the value of $x$? enter the correct value in the box.
show hints
$x = \square$

Explanation:

Step1: Recall midpoint property

Since \( E \) is the midpoint of \( \overline{DF} \), then \( DE = EF \) and \( DF = 2 \times DE \).

Step2: Substitute known values

We know \( DF = 4x + 2 \) and \( DE = 17 \), so \( DF = 2\times17 = 34 \). Thus, we set up the equation \( 4x + 2 = 34 \).

Step3: Solve for \( x \)

Subtract 2 from both sides: \( 4x = 34 - 2 = 32 \). Then divide both sides by 4: \( x=\frac{32}{4}=8 \).

Answer:

\( 8 \)