Question

Which statements are true about the solution to the inequality 10≥22+x
? Select the three correct answers.



(3 points)
Responses

The graph has an open circle.
The graph has an open circle.

x≤−12
x is less than or equal to negative 12

The graph has a closed circle.
The graph has a closed circle.

-11 is part of the solution
-11 is part of the solution

x≥−12
x is greater than or equal to negative 12

-13 is part of the solution

Answer 1

To solve the inequality \(10 \geq 22 + x\), we can start by isolating \(x\):

1. Subtract 22 from both sides:
\[
10 - 22 \geq x
\]
This simplifies to:
\[
-12 \geq x
\]
or equivalently,
\[
x \leq -12
\]

Now, let's evaluate the statements based on the solution \(x \leq -12\):

1. **The graph has an open circle.** - **False**
- Since the inequality is "less than or equal to", the endpoint \(-12\) is included in the solution, which means we use a closed circle.

2. **x ≤ -12** - **True**
- This is the correct interpretation of our solution.

3. **The graph has a closed circle.** - **True**
- Because \(-12\) is included in the solution, we use a closed circle on the graph.

4. **-11 is part of the solution.** - **False**
- \(-11\) does not satisfy \(x \leq -12\).

5. **x ≥ -12** - **False**
- This is incorrect since the correct inequality is \(x \leq -12\).

6. **-13 is part of the solution.** - **True**
- Since \(-13 < -12\), it satisfies the inequality \(x \leq -12\).

In summary, the three correct answers are:
- **x ≤ -12**
- **The graph has a closed circle.**
- **-13 is part of the solution.**