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Let's solve the inequalities step by step.

### First Inequality:
\[ 7x + 3 < 4 \]

1. Subtract 3 from both sides:
\[ 7x < 1 \]

2. Divide both sides by 7:
\[ x < \frac{1}{7} \]

### Second Inequality:
\[ x + 9 > 13 \]

1. Subtract 9 from both sides:
\[ x > 4 \]

### Final Solution:
The solution to the inequality is:
\[ x < \frac{1}{7} \quad \text{or} \quad x > 4 \]

For the fill-in-the-blank section:
- The first box should contain \( \frac{1}{7} \)
- The second box should contain \( 4 \)

Would you like more details or have any other questions?

### Related Questions:
1. How would the solution change if the inequalities were "and" instead of "or"?
2. Can you graph the solution set on a number line?
3. How do you solve compound inequalities involving "and"?
4. What happens if you multiply or divide an inequality by a negative number?
5. How can you check your solutions to inequalities?

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

Solve the inequality: 7x + 3 < 4 or x + 9 > 13

Learn how to solve the inequality 7x + 3 < 4 or x + 9 > 13 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving inequalities by isolating x and understanding when to reverse inequality signs. Suitable for students in Grades 7-9.

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