Question

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



(3 points)
Responses

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

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

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

The 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

To solve the inequality \( 10 \geq 22 + x \), we can rearrange it as follows:

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

Now we can evaluate the statements given:

1. **\( x \leq -12 \)** - This is **true**.
2. **\( x \geq -12 \)** - This is **false**.
3. **-11 is part of the solution** - This is **false** because \(-11\) is greater than \(-12\).
4. **The graph has a closed circle** - This is **true** because the solution includes \(-12\) (the inequality is \(\leq\)).
5. **The graph has an open circle** - This is **false**.
6. **-13 is part of the solution** - This is **true** because \(-13\) is less than \(-12\).

Thus, the three correct statements are:

1. \( x \leq -12 \)
2. The graph has a closed circle.
3. -13 is part of the solution.