Question

on a line segment, e is between d and f. if de = 20, ef = 14x, and df = 18x + 16, what is df? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment - addition postulate

Since $E$ is between $D$ and $F$, $DE + EF=DF$. Substitute the given expressions: $20 + 14x=18x + 16$.

Step2: Solve for $x$

Subtract $14x$ from both sides: $20=18x - 14x+16$, which simplifies to $20 = 4x+16$. Then subtract 16 from both sides: $20 - 16=4x$, so $4 = 4x$. Divide both sides by 4, we get $x = 1$.

Step3: Find the value of $DF$

Substitute $x = 1$ into the expression for $DF$. Since $DF=18x + 16$, then $DF=18\times1+16$. Calculate $18\times1+16=18 + 16=34$.

Answer:

34