Q36.

For the following figure, $E$ is the midpoint of $\bar{D F}$ . Find the value $x$ , where $D E = 2 x - 3$ and $E F = 5 x - 24$

Verified

Answer

The value of $x$ is 7.

1Step 1. Apply the concept of midpoint .

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

2Step 2. Check the figure.

Consider the figure.

Here $E$ is the midpoint of $\bar{D F}$ .

Therefore $D E = E F$ .

3Step 3. Find the value of x .

Since $D E = E F$ .

Equate the values as follows:

$2 x - 3 = 5 x - 24$

4Step 4. Simplify the equation.

Simplify the equation as follows:

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

Therefore, the value of $x$ is 7.