Question

question point d is on line segment $overline{ce}$. given $de = x + 10, cd = 6$, and $ce = 3x$, determine the numerical length of $overline{de}$.

Explanation:

Step1: Use segment - addition postulate

Since point $D$ is on line segment $\overline{CE}$, we have $CD + DE=CE$. Substituting the given expressions: $6+(x + 10)=3x$.

Step2: Simplify the left - hand side

Combine like terms: $6+x + 10=x+16$. So the equation becomes $x + 16=3x$.

Step3: Solve for $x$

Subtract $x$ from both sides: $16=3x - x$, which simplifies to $16 = 2x$. Then divide both sides by 2: $x=\frac{16}{2}=8$.

Step4: Find the length of $DE$

Substitute $x = 8$ into the expression for $DE$. Since $DE=x + 10$, then $DE=8 + 10=18$.

Answer:

18