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?

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!