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 solutionx≤−12x is less than or equal to negative 12x≥−12x is greater than or equal to negative 12The graph has a closed circle.The graph has a closed circle.The graph has an open circle.The graph has an open circle.-13 is part of the solution

Answer 1

Let's solve the inequality step by step:

The inequality is:

\[ 10 \geq 22 + x \]

First, we want to isolate \( x \):

1. Subtract 22 from both sides:

\[ 10 - 22 \geq x \]

This simplifies to:

\[ -12 \geq x \]

or equivalently,

\[ x \leq -12 \]

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

1. **-11 is part of the solution**: **False**. Since -11 is greater than -12, it does not satisfy \( x \leq -12 \).

2. **x ≤ −12**: **True**. This is the main inequality we derived.

3. **x is less than or equal to negative 12**: **True**. This statement is essentially the same as the previous one.

4. **x ≥ -12**: **False**. This contradicts the solution.

5. **The graph has a closed circle**: **True**. For \( x \leq -12 \), a closed circle is used to indicate that -12 is included in the solution.

6. **The graph has an open circle**: **False**. Open circles are used for inequalities that do not include the endpoint.

7. **-13 is part of the solution**: **True**. Since -13 is less than -12, it satisfies \( x \leq -12 \).

From the analysis:

- **True statements**:
- x ≤ −12
- x is less than or equal to negative 12
- The graph has a closed circle
- -13 is part of the solution

So, the three correct answers from the given options about the solution to the inequality are:

1. **x ≤ −12**
2. **x is less than or equal to negative 12**
3. **The graph has a closed circle**

If you're restricted to selecting only three answers total, just choose any three from the true indicators above.