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.
Solve for xx and graph the solution on the number line below.
12>x+9≥-1
1 answer