Solve the following inequality. Graph and check your solution.
15z<-45
Solve the inequality.
To solve the inequality, we can divide both sides of the inequality by 15:
z < -45/15
Simplifying the right side gives:
z < -3
To graph the solution, we can draw a number line and mark an open circle at -3 to represent that it is not included in the solution. We then shade the region to the left of -3 to indicate all the values less than -3.
To check the solution, we can choose a test value, such as z = -4, and substitute it into the original inequality:
15z < -45
15(-4) < -45
-60 < -45
Since -60 is less than -45, the inequality is true. Therefore, the solution is correct.
Graphically, the solution would look like this:
<----------------------------------o~~~~~~~~~~~