Choose the correct solution and graph for the inequality.
Z+9≤6
The correct solution for the inequality Z + 9 ≤ 6 is Z ≤ -3.
Graphically, this inequality represents all real numbers less than or equal to -3 on a number line.
To solve the inequality Z + 9 ≤ 6, we need to isolate Z on one side of the inequality symbol.
Step 1: Subtract 9 from both sides of the inequality:
Z + 9 - 9 ≤ 6 - 9
Z ≤ -3
Step 2: Graphing the solution:
To graph the solution, we need to plot all values of Z that are less than or equal to -3 on a number line. We represent -3 as a closed circle because the inequality includes "less than or equal to". Then, we draw a line from -3 extending towards negative infinity, as the solution includes all values less than or equal to -3.
Here is a graph representing the solution:
-∞ -3
─┈┈┈┈◯━━━
Now, we have the solution Z ≤ -3 and its graph.
To solve this inequality, we need to isolate the variable Z on one side of the inequality sign.
First, let's subtract 9 from both sides of the inequality:
Z + 9 - 9 ≤ 6 - 9
This simplifies to:
Z ≤ -3
Now we have the solution: Z is less than or equal to -3.
To graph this solution on a number line, you would plot a closed circle at -3 (since it includes -3 in the solution), and shade to the left of -3. This represents all the values of Z that are less than or equal to -3.
Here is a visual representation of the graph:
```
-∞ -3
─────┃•━━━━━━━
```
The closed circle indicates that -3 is included in the solution, and the shading to the left of -3 represents all the values that satisfy the inequality Z + 9 ≤ 6.