Solve for xx and graph the solution on the number line below.

12>x+9≥-1

1 answer

To solve for xx, let's start by solving the inequality in two parts since we have a compound inequality.

First, let's solve 12 > x + 9:

12 > x + 9
Subtract 9 from both sides to isolate x:
12 - 9 > x
3 > x

This means that x must be less than 3.

Next, let's solve x + 9 ≥ -1:

x + 9 ≥ -1
Subtract 9 from both sides to isolate x:
x ≥ -1 - 9
x ≥ -10

This means that x must be greater than or equal to -10.

Now let's combine these two inequalities to find the range for x.

-10 ≤ x < 3

This means that x can take any value between -10 and 3, including -10 but not including 3.

To graph the solution on a number line:

```
-10 0 3
---------|------------------|------------------|---------
[===================)
```

Explanation of the number line:
- The bracket '[' at -10 means -10 is included in the solution set (x ≥ -10).
- The parenthesis ')' at 3 means that 3 is not included in the solution set (x < 3).
- The line '===' between -10 and 3 represents all the values that x can take.

Remember, the variable in the original problem you've asked is 'xx', so replace x with 'xx' if that is the exact variable you intended to solve for. However, I'll refer to it just as 'x' since it is more common and for clarity's sake.