Solve the system of inequalities by graphing.
x>-7
x≤5
Select a line to change it between solid and dotted. Select a region to shade it.
To solve the system of inequalities, we will graph each inequality on the coordinate plane.
1) The inequality x > -7 represents a line that is dotted and does not include -7.
To graph this, we draw a dotted vertical line passing through -7 on the x-axis. Since the inequality is only greater than -7, we do not include -7 in the solution.
2) The inequality x ≤ 5 represents a line that is solid and includes 5.
To graph this, we draw a solid vertical line passing through 5 on the x-axis. Since the inequality is less than or equal to 5, we include 5 in the solution.
The graph will look like this:
5|
|
------|---
|
-7|
We shade the region to the left of -7 (excluding -7) and up to and including 5. This shaded region represents the solution to the system of inequalities.
Answer: The shaded region to the left of -7 (excluding -7) and up to and including 5 is the solution to the system of inequalities.