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To solve the given absolute value inequality:

\[
|9x + 10| < 40
\]

we need to rewrite it as two linear inequalities without the absolute value. The property of absolute value inequalities states that if \(|A| < B\), then:

\[
-B < A < B
\]

Applying this to our inequality:

\[
-40 < 9x + 10 < 40
\]

Now, we solve these two inequalities separately:

1. **For the left inequality:**  
   \[
   -40 < 9x + 10
   \]
   Subtract 10 from both sides:
   \[
   -50 < 9x
   \]
   Divide by 9:
   \[
   -\frac{50}{9} < x
   \]

2. **For the right inequality:**  
   \[
   9x + 10 < 40
   \]
   Subtract 10 from both sides:
   \[
   9x < 30
   \]
   Divide by 9:
   \[
   x < \frac{30}{9} \implies x < \frac{10}{3}
   \]

The two linear inequalities are:

\[
-\frac{50}{9} < x \quad \text{and} \quad x < \frac{10}{3}
\]

Since both conditions need to be true at the same time, we use the conjunction "and" to join them.

The final solution is:

\[
-\frac{50}{9} < x \text{ and } x < \frac{10}{3}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you solve absolute value inequalities with "greater than" (|A| > B)?
2. What are some methods to solve compound inequalities?
3. How can you graph the solution set of \(-\frac{50}{9} < x < \frac{10}{3}\)?
4. What is the difference between using "and" vs. "or" in inequalities?
5. How can you convert an absolute value equation to a linear equation?

**Tip:** When dealing with absolute value inequalities, always check if the expression is less than, greater than, or equal to the constant, as it determines the nature of the solution (conjunction or disjunction).

Rewrite the absolute value inequality |9x + 10| < 40 as two linear inequalities.

Learn how to rewrite the absolute value inequality |9x + 10| < 40 as two linear inequalities. This problem covers concepts like absolute value properties and solving compound inequalities. Suitable for students in Grades 9-11.

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