Question

Which statements are true about the solution to the inequality 15≥22+x?

- The graph has a closed circle.
- -7 is part of the solution
- x ≤ -7
- The graph has an open circle
- x ≥ -7
- -6 is part of the solution

Answer 1

To solve the inequality \( 15 \geq 22 + x \), we first isolate \( x \):

1. Subtract 22 from both sides:
\[
15 - 22 \geq x
\]
This simplifies to:
\[
-7 \geq x
\]
or equivalently,
\[
x \leq -7
\]

Now let's evaluate the statements provided:

1. **The graph has a closed circle.** - **True**: The inequality \( x \leq -7 \) includes -7, so the graph will show a closed circle at -7.

2. **-7 is part of the solution.** - **True**: Since \( x \) can be equal to -7 (as indicated by the \( \leq \) symbol), -7 is part of the solution set.

3. **x ≤ -7.** - **True**: This is exactly what we found from solving the inequality.

4. **The graph has an open circle.** - **False**: Since -7 is included in the solution, there should be a closed circle, not an open circle.

5. **x ≥ -7.** - **False**: The correct part of the solution is \( x \leq -7\), not \( x \geq -7\).

6. **-6 is part of the solution.** - **False**: Since -6 is greater than -7, it is not included in the solution set \( x \leq -7\).

In summary, the true statements are:
- The graph has a closed circle.
- -7 is part of the solution.
- \( x \leq -7 \).