Question

Which statements are true about the solution to the inequality 10<14+x
? Select the three correct answers.



(3 points)
Responses

x<−4
x<−4

x>−4
x is greater than negative 4

-4 is part of the solution
-4 is part of the solution

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

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

-3 is part of the solution

Answer 1

To solve the inequality \(10 < 14 + x\), we can rearrange it to isolate \(x\):

1. Subtract 14 from both sides:
\[
10 - 14 < x
\]
\[
-4 < x
\]

This can also be expressed as:
\[
x > -4
\]

Now we can analyze the statements:

1. **\(x < -4\)** - **False**. The solution corresponds to \(x > -4\).

2. **\(x > -4\)** - **True**. This matches our obtained solution.

3. **\(-4\) is part of the solution** - **False**. Since the inequality is strict (\(>\)), \(-4\) is not included in the solution.

4. **The graph has an open circle** - **True**. Since \(-4\) is not included in the solution, we would represent it with an open circle on a number line.

5. **The graph has a closed circle** - **False**. A closed circle would indicate that the endpoint is included, which is not the case here.

6. **\(-3\) is part of the solution** - **True**. As \(-3\) is greater than \(-4\), it is indeed part of the solution set.

Based on this analysis, the three correct answers are:

- **\(x > -4\)**
- **The graph has an open circle.**
- **\(-3\) is part of the solution.**