Step-by-step solution:

We are given two inequalities to solve for $b$:

1. $b - 4 > 6$
2. $b - 6 < 2$

Inequality 1: $b - 4 > 6$

Add 4 to both sides: $b > 6 + 4$ $b > 10$

Inequality 2: $b - 6 < 2$

Add 6 to both sides: $b < 2 + 6$ $b < 8$

Combining the results:

We have two cases:

• $b > 10$
• $b < 8$

This is an "or" condition, meaning the solution includes values for $b$ that satisfy either inequality.

Final solution:

The solution set for $b$ is:

• $b < 8$, or
• $b > 10$

Graph:

• The interval $b < 8$ is represented by a ray pointing to the left, starting from $b = 8$ and excluding 8 (open circle at 8).
• The interval $b > 10$ is represented by a ray pointing to the right, starting from $b = 10$ and excluding 10 (open circle at 10).

Would you like more details on graphing, or do you have any questions?

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Here are some questions that expand on this:

1. What happens if the inequality is "and" instead of "or"?
2. How would the solution change if one inequality had an equal sign (e.g., $\geq$ or $\leq$)?
3. How can this problem be visualized on a number line using set notation?
4. What does it mean if two inequalities have no overlapping solution?
5. How can compound inequalities be applied in real-world problems?

Tip: Always plot the critical points first, then check the direction of the inequality for accurate graphing.