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To solve for \( x \) and ensure that lines \( A \) and \( B \) are parallel, we need to use the fact that the corresponding angles formed by a transversal with two parallel lines must be equal.

Given:
- The angle on line \( A \) is \( 9x + 24 \).
- The corresponding angle on line \( B \) is \( 3x \).

For lines \( A \) and \( B \) to be parallel, the corresponding angles must be equal:
\[
9x + 24 = 3x
\]

Now, let's solve for \( x \):

\[
9x + 24 = 3x
\]

Subtract \( 3x \) from both sides:

\[
6x + 24 = 0
\]

Subtract 24 from both sides:

\[
6x = -24
\]

Divide by 6:

\[
x = -4
\]

The solution is:
\[
x = -4
\]

Would you like further details or have any other questions?

### Related Questions:
1. What are the corresponding angles, and why do they need to be equal for lines to be parallel?
2. What would happen if the value of \( x \) did not satisfy this equation?
3. How do we identify corresponding angles in different geometric configurations?
4. Can you provide a real-world example where parallel lines and corresponding angles are relevant?
5. How do different types of angles (alternate interior, exterior, etc.) behave with parallel lines?

**Tip:** Remember that in geometry, parallel lines have equal corresponding angles when crossed by a transversal.

Solve for x to make lines A and B parallel, where the angle on line A is 9x + 24, and the corresponding angle on line B is 3x.

Learn how to solve for x to make lines A and B parallel by equating corresponding angles formed by a transversal. This problem covers algebra and geometry, including the concept of parallel lines and corresponding angles. Suitable for students in Grades 8-10.

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