Choose the correct solution and graph for the inequality.
z-6<-14
The correct solution is: z < -8
Graph:
------o----------------
To solve the inequality z - 6 < -14, we need to isolate the variable z. Here are the steps:
Step 1: Add 6 to both sides of the inequality:
z - 6 + 6 < -14 + 6
z < -8
The solution to the inequality is z < -8.
To graph this on a number line, we can plot an open circle at -8 (since the inequality is less than, not less than or equal to) and shade the line to the left of -8 to represent all the values that are less than -8.
Here's an example of what the graph would look like:
o
<===============|--->
-9 -8 -7 -6
The open circle at -8 indicates that -8 is not included in the solution set, and the shaded line to the left represents all values less than -8.
To solve the inequality z - 6 < -14, you can follow these steps:
1. Add 6 to both sides of the inequality to isolate the variable z:
z - 6 + 6 < -14 + 6
z < -8
2. Now that you have the simplified inequality z < -8, you can graph the solution on a number line.
Start by drawing a number line and marking -8 on it.
-8 (marked on the number line)
Since the inequality is less than (-8 is not included), draw an open circle at -8 to represent the boundary not being included.
o -8
Finally, shade the region to the left of -8 to represent all the values that make the inequality true.
o x < -8
←−−−−−−−−−−−−−−−−−−−
So, the graph for the inequality z - 6 < -14 is a number line where the shaded region is to the left of an open circle at -8.