Question

point d is on line segment $overline{ce}$. given $de = x + 10, cd = 6$, and $ce = 3x$, determine the numerical length of $overline{de}$. answer attempt 1 out of 2 $de =$

Explanation:

Step1: Use segment - addition postulate

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

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for x

Subtract x from both sides: $16=3x−x$. Then $16 = 2x$. Divide both sides by 2: $x=\frac{16}{2}=8$.

Step4: Find the length of $\overline{DE}$

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

Answer:

$18$