Solve for b and graph the solution.
b–4>6 or b–6<2
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

### 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.

Solve for b and graph the solution. b–4>6 or b–6<2. Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

Learn how to solve and graph the linear inequalities b - 4 > 6 and b - 6 < 2 with a step-by-step solution. Understand how to plot open endpoints and represent the solution on a number line. Suitable for students in Grades 6-8.

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