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To solve for \( x \) such that lines \( A \parallel B \), we can apply the concept of corresponding angles. Since \( A \parallel B \), the angles created by the transversal must be equal.

In the diagram, the angles corresponding to lines \( A \) and \( B \) are labeled as:
- For line \( A \): \( 3x + 3 \)
- For line \( B \): \( 16x + 6 \)

Since these angles must be equal for the lines to be parallel, we set the expressions equal to each other and solve for \( x \):

\[
3x + 3 = 16x + 6
\]

### Step-by-step solution:

1. Subtract \( 3x \) from both sides:
   \[
   3 = 13x + 6
   \]

2. Subtract 6 from both sides:
   \[
   -3 = 13x
   \]

3. Divide by 13:
   \[
   x = \frac{-3}{13}
   \]

So, the solution is:

\[
x = -\frac{3}{13}
\]

Would you like further explanation on any step? 

### Related Questions:
1. What are corresponding angles and how are they used to determine parallel lines?
2. How can the properties of transversals help in solving geometry problems involving parallel lines?
3. Can lines be parallel even if the transversal forms unequal angles? Why or why not?
4. How do we apply the slope concept to determine if two lines are parallel?
5. What are some real-life applications of parallel lines and transversal concepts?

### Tip:
When dealing with parallel lines, always check if the angles formed by a transversal are equal, as this will confirm their parallelism.

Solve for x to make A parallel to B, given the expressions for the angles formed by the transversal are 3x + 3 for line A and 16x + 6 for line B.

Learn how to solve for x to make two lines parallel by using the concept of corresponding angles. This problem involves algebraic expressions and properties of parallel lines, suitable for students in Grades 8-10.

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