Question

if de = 11x, ef = 17x - 12, 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: $16=11x+(17x - 12)$.

Step2: Simplify the right - hand side

Combine like terms: $16 = 11x+17x-12$, which simplifies to $16=28x - 12$.

Step3: Solve for $x$

Add 12 to both sides of the equation: $16 + 12=28x-12 + 12$, so $28 = 28x$. Then divide both sides by 28, getting $x = 1$.

Step4: Find $DE$

Substitute $x = 1$ into the expression for $DE$. Since $DE = 11x$, then $DE=11\times1=11$.

Answer:

11