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We are asked to solve for \( x \) in the inequality:

\[
y < mx + b
\]

### Step-by-step solution:

1. **Isolate** \( mx \) on one side:
   \[
   y - b < mx
   \]
   (Subtract \( b \) from both sides).

2. **Solve for** \( x \):
   \[
   \frac{y - b}{m} < x
   \]
   (Divide both sides by \( m \)).

This gives us:

\[
x > \frac{y - b}{m}
\]

So, the correct answer is the last option: 
\[
x > \frac{y - b}{m}
\]

Would you like further details or have any questions about this solution?

Here are 5 related questions for deeper understanding:

1. What happens if the inequality was \( y > mx + b \)?
2. How does the solution change if \( m \) is negative?
3. Can you graph the inequality \( y < mx + b \) and interpret the solution visually?
4. What are the steps to solve for \( x \) in an absolute value inequality?
5. How would you solve for \( x \) if \( b = 0 \)?

**Tip:** When solving inequalities, be cautious about the direction of the inequality sign, especially when dividing by a negative number.

Learn how to solve the linear inequality y < mx + b for x. This step-by-step guide helps you understand key algebraic concepts and how to rearrange the inequality. Ideal for students in Grades 9-12.

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