https://file.aiquickdraw.com/mathbot/file/1727453100338d0tm9oam.jpg

From the image, I can see two inequalities written in Arabic numerals, which I'll interpret as follows:

1. The first inequality appears to be:

\[
x - 1 > 4
\]

2. The second inequality seems to be:

\[
x + 1 < 2
\]

Now, let's solve these inequalities one by one.

### Inequality 1: \( x - 1 > 4 \)
Add 1 to both sides:

\[
x > 4 + 1
\]

\[
x > 5
\]

### Inequality 2: \( x + 1 < 2 \)
Subtract 1 from both sides:

\[
x < 2 - 1
\]

\[
x < 1
\]

### Solution
The solution to these two inequalities is that \(x\) must satisfy **both** conditions: \(x > 5\) and \(x < 1\). 

However, there's no number \(x\) that is both greater than 5 and less than 1, so **no solution exists** where these two inequalities are true simultaneously.

Let me know if you would like more details or if you have further questions.

Here are 5 relative questions:
1. How do we represent inequalities on a number line?
2. Can inequalities have a solution with no overlap, as in this case?
3. What are the rules for solving compound inequalities?
4. How would the solution change if the inequalities were non-strict (i.e., \( \geq \) and \( \leq \))?
5. Can you think of a scenario where such inequalities would have a real-life application?

**Tip:** Always check for contradictions when solving inequalities to avoid incorrect conclusions!

Solve the inequalities: x - 1 > 4 and x + 1 < 2

Learn how to solve compound inequalities, including x - 1 > 4 and x + 1 < 2, using algebraic methods. This step-by-step guide covers key concepts in inequalities, suitable for students in Grades 7-9.

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