Let's solve the inequality step by step:
-
Start with the inequality:
\( x + 8 > 10 \) -
Subtract 8 from both sides:
\( x > 10 - 8 \)
\( x > 2 \)
So, the solution to the inequality \( x + 8 > 10 \) is \( x > 2 \).
Now, looking at the additional inequalities you provided:
- \( x < 2 \)
- \( x > 18 \)
- \( x < 18 \)
- \( x > 2 \)
From this, we see that:
- \( x > 2 \) is valid and aligns with the condition we derived from \( x + 8 > 10 \).
- \( x < 2 \) contradicts \( x > 2 \), so it's not valid.
- \( x > 18 \) does not contradict \( x > 2 \), but it is a more specific condition.
- \( x < 18 \) can be valid, but it’s less specific.
Therefore, the only condition that aligns with \( x + 8 > 10 \) is \( x > 2 \). If we take \( x > 18 \) into account (as it is more restrictive than \( x > 2 \)), then \( x \) should satisfy both. So, the system of inequalities would ultimately suggest the valid solution is:
Valid range: \( x > 18 \).