To solve the inequality 13 < 5x + 2 < 28, we start by breaking it into two parts: 5x + 2 > 13 and 5x + 2 < 28.
1. For the first part, 5x + 2 > 13:
- Subtract 2 from both sides: 5x > 11
- Now divide by 5: x > 11/5 or x > 2.2.
2. For the second part, 5x + 2 < 28:
- Again, subtract 2 from both sides: 5x < 26
- Now divide by 5: x < 26/5 or x < 5.2.
Now we combine the two parts of the inequality: 2.2 < x < 5.2.
On a number line, this means:
- The graph should have an open dot at 2.2 (which is the same as 11/5) and another open dot at 5.2 (which is the same as 26/5).
- All the values between 2.2 and 5.2 are included, but not the endpoints themselves since we are dealing with open dots.
If the graph in question has open dots placed at 3 and 6, then it is incorrect. The correct graph would have open dots around the values of 2.2 and 5.2, capturing the interval of values that satisfy the inequality. Therefore, you will be looking for a graph that reflects the range of values between these two points on the number line.