Let's solve these inequalities one by one:

### First inequality: 
\[
5x - 1 > 4
\]

1. Add 1 to both sides to eliminate the \(-1\) on the left side:
\[
5x > 5
\]

2. Divide both sides by 5 to solve for \(x\):
\[
x > 1
\]

### Second inequality:
\[
x + 1 < 3
\]

1. Subtract 1 from both sides to solve for \(x\):
\[
x < 2
\]

### Final solution:
We now have the two inequalities \(x > 1\) and \(x < 2\). Combining these, we get the solution:
\[
1 < x < 2
\]
So, the solution is \(x\) is between 1 and 2 (but not equal to 1 or 2).

Do you want further details or have any questions?

Here are 5 related questions you can try:
1. Solve \(3x + 4 > 7\) and \(x - 2 < 0\).
2. What is the solution to \(2x - 5 \leq 1\) and \(x + 3 \geq 0\)?
3. How do you solve a compound inequality?
4. What is the difference between strict inequalities and inclusive inequalities?
5. How do you graph the solution of \(1 < x < 2\)?

**Tip:** When solving inequalities, always remember that multiplying or dividing by a negative number reverses the inequality sign!

Learn how to solve the compound inequality 5x − 1 > 4 and x + 1 < 3 step-by-step. Understand key algebraic concepts such as linear inequalities and the properties of inequalities. Suitable for students in Grades 6-8.

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