Question

if de = x + 2, ef = 2, and df = 5x, what is de? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $DF=DE + EF$, we substitute the given expressions: $5x=(x + 2)+2$.

Step2: Simplify the right - hand side

$5x=x + 4$.

Step3: Solve for $x$

Subtract $x$ from both sides: $5x−x=x + 4−x$, which gives $4x=4$. Then divide both sides by 4: $x = 1$.

Step4: Find the value of $DE$

Substitute $x = 1$ into the expression for $DE$. Since $DE=x + 2$, then $DE=1+2=3$.

Answer:

3