Question

the length of $overline{df}$ is 8. find the length of $overline{de}$.
draw
$d$ ---- $2x + 1$ ---- $e$ ---- $2x + 3$ ---- $f$
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Explanation:

Step1: Set up the equation for DF

Since \( DF = DE + EF \), substitute \( DE = 2x + 1 \), \( EF = 2x + 3 \), and \( DF = 8 \). So, \( (2x + 1) + (2x + 3) = 8 \).

Step2: Simplify and solve for x

Combine like terms: \( 4x + 4 = 8 \). Subtract 4 from both sides: \( 4x = 4 \). Divide by 4: \( x = 1 \).

Step3: Find the length of DE

Substitute \( x = 1 \) into \( DE = 2x + 1 \): \( DE = 2(1) + 1 = 3 \).

Answer:

3