Question

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



(3 points)
Responses

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

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

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

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

-13 is part of the solution
-13 is part of the solution

x≤−12

Answer 1

To solve the inequality \(10 \geq 22 + x\), we first isolate \(x\):

1. Subtract 22 from both sides:
\[ 10 - 22 \geq x \]
\[ -12 \geq x \]
This can also be written as:
\[ x \leq -12 \]

Now, let's analyze the given statements:

1. **-11 is part of the solution**:
- Since \(-11 > -12\), this statement is **false**.

2. **The graph has a closed circle**:
- Since the inequality is \(x \leq -12\), we would represent this with a closed circle at \(-12\) on a number line. This statement is **true**.

3. **x ≥ −12**:
- This is the opposite of what we found. The solution is \(x \leq -12\), not \(x \geq -12\). This statement is **false**.

4. **The graph has an open circle**:
- Because the solution includes \(-12\) (closed at \(-12\)), this statement is **false**.

5. **-13 is part of the solution**:
- Since \(-13 < -12\), this statement is **true**.

6. **x ≤ −12**:
- This is exactly what we found from solving the inequality, so this statement is **true**.

Therefore, the three correct answers are:

- The graph has a closed circle.
- -13 is part of the solution.
- x ≤ −12.