Let's solve this step by step to determine which equation correctly models the situation:
1. Understanding the problem:
- Keenan currently does 8 pushups each day.
- He increases the number of pushups by 2 pushups every day.
- He wants to eventually do 30 pushups each day.
- We need to find [tex]\(x\)[/tex], the number of days it will take to reach 30 pushups.
2. Analyzing each option:
Option (A): [tex]\(8 + 2x = 30\)[/tex]
- Starting with 8 pushups and adding 2 pushups each day, multiplied by [tex]\(x\)[/tex] days seems like a reasonable way to model the problem.
- After [tex]\(x\)[/tex] days, the number of pushups done each day can be expressed as [tex]\(8 + 2x\)[/tex].
- This equation appears to fit the scenario well.
Option (B): [tex]\((8 + 2)x = 30\)[/tex]
- This equation indicates that Keenan is doing [tex]\((8 + 2)\)[/tex], or 10 pushups each day, from the very start, which doesn't match the problem statement.
Option (C): [tex]\(8(2 + x) = 30\)[/tex]
- This equation suggests Keenan does 8 pushups multiplied by [tex]\((2 + x)\)[/tex], but given the problem details, this doesn't make sense. It implies an incorrect daily increase.
Option (D): [tex]\(8 + 2 + x = 30\)[/tex]
- This indicates starting with 8 pushups, adding 2, and then adding [tex]\(x\)[/tex]. It does not correctly represent the daily increase of 2 pushups.
3. Conclusion:
- The equation that correctly models the situation is [tex]\(8 + 2x = 30\)[/tex].
Thus, the answer is:
(A) [tex]\(8 + 2x = 30\)[/tex]
