Select the equation needed to solve the following word problem:

Kayla is sending invitations to 20 of her friends for a pizza party. If there are 12 invitations left to send out, how many invitations has she already mailed?

A. [tex]x - 8 = 20[/tex]
B. [tex]x + 8 = 12[/tex]
C. [tex]x + 20 = 12[/tex]
D. [tex]x + 12 = 20[/tex]

To solve the problem, we need to find out how many invitations Kayla has already mailed.

1. Understand the Problem:
- Kayla is sending invitations to a total of 20 friends.
- There are 12 invitations left to send.

2. Define the Variable:
- Let [tex]$ x $[/tex] represent the number of invitations Kayla has already mailed.

3. Set Up the Equation:
- Since there are 20 invitations in total and Kayla has 12 left to send, the equation representing the scenario is:
[tex]\[
x + 12 = 20
\][/tex]

4. Solve the Equation:
- To find [tex]$ x $[/tex], solve the equation:
[tex]\[
x + 12 = 20
\][/tex]
- Subtract 12 from both sides:
[tex]\[
x = 20 - 12
\][/tex]
- Calculate:
[tex]\[
x = 8
\][/tex]

This means Kayla has already mailed 8 invitations.

The correct choice from the given options is D. [tex]$ x + 12 = 20 $[/tex].