What is the correct graph for the compound inequality. -7<x<15

To graph the compound inequality \(-7 < x < 15\), you need to plot a number line and show the range of values for \(x\) that satisfy the inequality.

Here’s how you can do it:

1. Draw a horizontal number line.
2. Identify and mark the points \(-7\) and \(15\) on the number line.
3. Since \(-7 < x\), place an open circle at \(-7\) to indicate that \(-7\) is not included in the solution.
4. Since \(x < 15\), place an open circle at \(15\) to indicate that \(15\) is not included in the solution.
5. Shade the region between \(-7\) and \(15\) to show all the values that \(x\) can take.

Here’s a step-by-step graphical representation:

```
   -∞    -7    0    15    +∞
    |----(----|----|----)----|
```

- The open circles at \(-7\) and \(15\) show that these values are not included in the solution.
- The shaded line between \(-7\) and \(15\) represents all the values that satisfy the inequality.

If you have any questions or need further details, please let me know.

Here are 8 related questions:

1. How would the graph change if the inequality was \(-7 \leq x < 15\)?
2. How would the graph change if the inequality was \(-7 < x \leq 15\)?
3. How do you graph the inequality \(-7 \leq x \leq 15\)?
4. What is the interval notation for the compound inequality \(-7 < x < 15\)?
5. How would you solve a compound inequality involving more than two inequalities?
6. How can you represent the solution set of a compound inequality on a coordinate plane?
7. What is the difference between an open circle and a closed circle on a number line?
8. How do you solve and graph inequalities involving absolute values?

**Tip:** When graphing inequalities, always pay attention to whether the inequality includes the boundary points (indicated by closed circles) or not (indicated by open circles).

Learn how to graph the compound inequality -7 < x < 15 step-by-step. Understand the concept of inequalities and number line graphing with open circles to represent excluded values and shading to indicate the solution set. Suitable for Grades 7-9.

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