Question

if de = 17, ef = 11x - 6, and df = 14x - 4, what is ef? 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: $14x - 4=17+(11x - 6)$.

Step2: Simplify the right - hand side

$17+(11x - 6)=11x+17 - 6=11x + 11$. So the equation becomes $14x - 4=11x + 11$.

Step3: Isolate the variable $x$

Subtract $11x$ from both sides: $14x-11x - 4=11x-11x + 11$, which simplifies to $3x - 4=11$. Then add 4 to both sides: $3x-4 + 4=11 + 4$, so $3x=15$.

Step4: Solve for $x$

Divide both sides by 3: $\frac{3x}{3}=\frac{15}{3}$, so $x = 5$.

Step5: Find the length of $EF$

Substitute $x = 5$ into the expression for $EF$. $EF=11x - 6=11\times5-6=55 - 6=49$.

Answer:

49