Question

if de = 3x, ef = 15x - 20, and df = 16, 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: $16 = 3x+(15x - 20)$.

Step2: Simplify the equation

Combine like - terms: $16=3x + 15x-20$, which becomes $16 = 18x-20$.

Step3: Solve for x

Add 20 to both sides of the equation: $16 + 20=18x$, so $36 = 18x$. Then divide both sides by 18, we get $x = 2$.

Step4: Find the value of DE

Since $DE = 3x$, substitute $x = 2$ into the expression for $DE$. So $DE=3\times2=6$.

Answer:

6