https://file.aiquickdraw.com/mathbot/file/1728916497205cwfeo0gs.jpg

The image shows the inequality:

\[
3(x - 1) < 2x + 1
\]

Let's solve this step by step.

### Step 1: Expand the left-hand side
Expand the term \( 3(x - 1) \):
\[
3(x - 1) = 3x - 3
\]
Now the inequality becomes:
\[
3x - 3 < 2x + 1
\]

### Step 2: Isolate \(x\)
To isolate \(x\), subtract \(2x\) from both sides:
\[
3x - 2x - 3 < 1
\]
This simplifies to:
\[
x - 3 < 1
\]

### Step 3: Solve for \(x\)
Now, add 3 to both sides to get \(x\) by itself:
\[
x < 1 + 3
\]
\[
x < 4
\]

### Final Answer:
The solution is:
\[
x < 4
\]

Would you like more details or have any other questions?

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Here are 5 related questions to expand on this topic:
1. How would the solution change if the inequality sign were \( \leq \) instead of \( < \)?
2. What is the significance of multiplying or dividing by a negative number in an inequality?
3. How would you solve the inequality if the right-hand side was more complex, like \( 2x^2 + 1 \)?
4. Can you graph the solution of the inequality \( 3(x - 1) < 2x + 1 \) on a number line?
5. How does solving inequalities differ from solving equalities?

**Tip**: Always remember, when multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be flipped!

Learn how to solve the linear inequality 3(x - 1) < 2x + 1 with a detailed step-by-step solution. This problem covers key algebraic concepts like linear inequalities and basic theorem properties. Suitable for students in Grades 8-10.

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