Let's solve the inequality:

Inequality:

$6x - 9 < 15$

Steps:

1. Add 9 to both sides: $6x - 9 + 9 < 15 + 9$ $6x < 24$

2. Divide both sides by 6: $x < \frac{24}{6}$ $x < 4$

Inequality Notation:

The solution in inequality form is: $x < 4$

Graphing on the Number Line:

To graph this on the number line:

• Draw an open circle at $x = 4$ (since it's a strict inequality, not $\leq$).
• Shade the number line to the left of 4 (all values less than 4).

Would you like more details or help with the graphing? Here are some related questions:

1. What would change if the inequality had been $\leq$ instead of $<$?
2. How would you graph the inequality if it were $x > 4$?
3. What happens if both sides of the inequality involve variables?
4. How do inequalities differ when dividing by negative numbers?
5. What are some real-life applications of solving inequalities?

Tip: When solving inequalities, remember that multiplying or dividing by a negative number flips the inequality symbol.