Find the area of the rectangle in terms of x using the given length and width.

To solve the problem, we need to find the area of the rectangle in terms of \( x \). The formula for the area of a rectangle is:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Step 1: Identify the given dimensions

- Length of the rectangle: \( 2x - 3 \)
- Width of the rectangle: \( x + 7 \)

Step 2: Apply the area formula

Substitute the given length and width into the area formula:

\[
\text{Area} = (2x - 3)(x + 7)
\]

Step 3: Expand the expression using the distributive property

To expand \( (2x - 3)(x + 7) \), we use the distributive property (also known as the FOIL method for binomials):

\[
(2x - 3)(x + 7) = 2x \cdot x + 2x \cdot 7 - 3 \cdot x - 3 \cdot 7
\]

Now, perform each multiplication:

\[
2x \cdot x = 2x^2
\]
\[
2x \cdot 7 = 14x
\]
\[
-3 \cdot x = -3x
\]
\[
-3 \cdot 7 = -21
\]

Step 4: Combine like terms

Add all the terms together:

\[
2x^2 + 14x - 3x - 21
\]

Combine the like terms \( 14x \) and \( -3x \):

\[
2x^2 + (14x - 3x) - 21 = 2x^2 + 11x - 21
\]

Final Answer:

The area of the rectangle in terms of \( x \) is:

\[
\boxed{2x^2 + 11x - 21}
\]