Choose the correct solution graph for the inequality.
8x + 2 ≥ 26 or 4x - 6 ≤ -26
The correct solution graph for the inequality is the graph that represents the points that satisfy both inequalities simultaneously. To find this solution graph, we need to solve each inequality separately and then plot the solutions on a number line.
1) Solve the first inequality: 8x + 2 ≥ 26
- Subtract 2 from both sides: 8x ≥ 24
- Divide both sides by 8 (since 8 is positive, we don't need to flip the inequality sign): x ≥ 3
2) Solve the second inequality: 4x - 6 ≤ -26
- Add 6 to both sides: 4x ≤ -20
- Divide both sides by 4 (since 4 is positive, we don't need to flip the inequality sign): x ≤ -5
Now, we can plot these solutions on a number line:
- Place a closed circle at x = 3 (since x is greater than or equal to 3).
- Place a closed circle at x = -5 (since x is less than or equal to -5).
- Draw a solid line between these two points to indicate that all points on this line are also solutions.
The correct solution graph would look like this:
```
------------------•-------------•--------------------------------
-infinity -5 3 +infinity
```
Therefore, the correct solution graph for the given inequality is the second option.