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

Let's solve the word problem step-by-step.

Kayla is sending invitations to a total of 20 of her friends for a pizza party. She has already sent out some of the invitations, and there are 12 invitations left to send out. We need to find out how many invitations she has already mailed.

1. Define the variables:
- Let [tex]$ x $[/tex] be the number of invitations Kayla has already mailed.
- Total number of invitations that Kayla plans to send is 20.
- Number of invitations left to send is 12.

2. Set up the equation:
- According to the problem, the total number of invitations (20) is equal to the number of invitations already mailed ([tex]$ x $[/tex]) plus the number of invitations left to send (12).

So, the equation will be:
[tex]\[ x + 12 = 20 \][/tex]

From the given options:
- A. [tex]$ x + 8 = 12 $[/tex] (This is not correct.)
- B. [tex]$ x - 8 = 20 $[/tex] (This is not correct.)
- C. [tex]$ x + 20 = 12 $[/tex] (This is not correct.)
- D. [tex]$ x + 12 = 20 $[/tex] (This is correct.)

Therefore, the correct equation needed to solve the word problem is:
[tex]\[ x + 12 = 20 \][/tex]

So, the correct answer is:
D. [tex]$ x + 12 = 20 $[/tex]