Answer :
Sure, let's solve the problem step-by-step:
1. Understand the Problem:
- Kayla is sending invitations to 20 of her friends for a pizza party.
- There are 12 invitations left to send out.
- We need to determine how many invitations she has already mailed.
2. Translate the Problem to an Equation:
- Let [tex]\( x \)[/tex] represent the number of invitations Kayla has already mailed.
- Originally, she had 20 invitations to send.
- If she has already mailed [tex]\( x \)[/tex] invitations, the remaining invitations should be [tex]\( 20 - x \)[/tex].
- We are told there are 12 invitations left to send out, so we set [tex]\( 20 - x = 12 \)[/tex].
3. Solving the Equation:
- [tex]\( 20 - x = 12 \)[/tex]
- To solve for [tex]\( x \)[/tex], we isolate [tex]\( x \)[/tex] on one side of the equation by subtracting 12 from both sides:
[tex]\[
20 - x = 12
\][/tex]
[tex]\[
20 - 12 = x
\][/tex]
[tex]\[
8 = x
\][/tex]
4. Conclusion:
- Kayla has already mailed 8 invitations.
5. Equation Choices:
- The equation that matches our problem-solving process is [tex]\( x + 12 = 20 \)[/tex] because it represents the number of invitations already mailed (x) plus the remaining invitations (12) equals the total number of invitations (20).
Therefore, the correct equation is:
- D. [tex]$x + 12 = 20$[/tex]
1. Understand the Problem:
- Kayla is sending invitations to 20 of her friends for a pizza party.
- There are 12 invitations left to send out.
- We need to determine how many invitations she has already mailed.
2. Translate the Problem to an Equation:
- Let [tex]\( x \)[/tex] represent the number of invitations Kayla has already mailed.
- Originally, she had 20 invitations to send.
- If she has already mailed [tex]\( x \)[/tex] invitations, the remaining invitations should be [tex]\( 20 - x \)[/tex].
- We are told there are 12 invitations left to send out, so we set [tex]\( 20 - x = 12 \)[/tex].
3. Solving the Equation:
- [tex]\( 20 - x = 12 \)[/tex]
- To solve for [tex]\( x \)[/tex], we isolate [tex]\( x \)[/tex] on one side of the equation by subtracting 12 from both sides:
[tex]\[
20 - x = 12
\][/tex]
[tex]\[
20 - 12 = x
\][/tex]
[tex]\[
8 = x
\][/tex]
4. Conclusion:
- Kayla has already mailed 8 invitations.
5. Equation Choices:
- The equation that matches our problem-solving process is [tex]\( x + 12 = 20 \)[/tex] because it represents the number of invitations already mailed (x) plus the remaining invitations (12) equals the total number of invitations (20).
Therefore, the correct equation is:
- D. [tex]$x + 12 = 20$[/tex]
