Question

the length of $overline{df}$ is 8. solve for $x$.
draw
$2x - 21$ (between $d$ and $e$), $3x - 31$ (between $e$ and $f$).
show your work here
$x =$

Explanation:

Step1: Set up the equation for DF

Since \( DF = DE + EF \), we have \( (2x - 21) + (3x - 31) = 8 \).

Step2: Combine like terms

Combine the \( x \)-terms and constant terms: \( 2x + 3x - 21 - 31 = 8 \), which simplifies to \( 5x - 52 = 8 \).

Step3: Solve for x

Add 52 to both sides: \( 5x = 8 + 52 \), so \( 5x = 60 \). Then divide by 5: \( x = \frac{60}{5} = 12 \).

Answer:

\( x = 12 \)