Question

For the following figure, $E$is the midpoint of $\overline{DF}$. Find the value $x$, where $DE=2x-3$and $EF=5x-24$

Short answer

The value of$x$ is 7.

Step-by-step solution

Step 1. Apply the concept of midpoint.

The midpoint of a line divides the line into two equal parts.

Step 2. Check the figure.

Consider the figure.

Here $E$is the midpoint of $\overline{DF}$.

Therefore $DE=EF$.

Step 3. Find the value of x.

Since $DE=EF$.

Equate the values as follows:

$2x-3=5x-24$

Step 4. Simplify the equation.

Simplify the equation as follows:

$\begin{array}{c}2x-3=5x-24\\ 2x-5x=-24+3\\ -3x=-21\\ x=7\end{array}$

Therefore, the value of$x$ is 7.