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 determine how many invitations Kayla has already mailed out. According to the problem, Kayla is sending out a total of 20 invitations, and there are 12 invitations left to send.

To find out how many invitations have already been mailed, we can use the information that the total number of invitations is the sum of those already mailed and those left to send.

Here's the step-by-step solution:

1. Identify the Total Invitations: The problem states that Kayla is sending a total of 20 invitations.

2. Identify the Invitations Left to Send: The problem tells us there are 12 invitations left to send.

3. Set Up the Equation: Since the total invitations is the number already mailed plus the number left to send, we can write the equation:
[tex]\[
\text{already mailed} + \text{invitations left} = \text{total invitations}
\][/tex]

4. Substitute the Known Values: Replace "invitations left" with 12 and "total invitations" with 20 in the equation:
[tex]\[
x + 12 = 20
\][/tex]

5. Solve for [tex]$ x $[/tex]: Subtract 12 from both sides of the equation to find the number of invitations already mailed.
[tex]\[
x = 20 - 12
\][/tex]
[tex]\[
x = 8
\][/tex]

Kayla has already mailed 8 invitations.

Therefore, the equation you need to solve the word problem is:
D. [tex]$ x + 12 = 20 $[/tex]