Question

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



(3 points)
Responses

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

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

x>−4
x is greater than negative 4

-3 is part of the solution
-3 is part of the solution

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

x<−4

Answer 1

Let's solve the inequality \(10 < 14 + x\).

1. Subtract 14 from both sides:
\[
10 - 14 < x
\]
which simplifies to
\[
-4 < x
\]
or
\[
x > -4
\]

Based on this solution, let’s determine which statements are true:

1. **The graph has a closed circle.** - **False**. The inequality is strict (\(>\)), indicating an open circle on the graph.

2. **The graph has an open circle.** - **True**. The inequality \(x > -4\) uses an open circle because -4 is not included in the solution.

3. **x > -4** - **True**. This is the result from solving the inequality.

4. **-3 is part of the solution** - **True**. Since -3 is greater than -4, it is included in the solution set.

5. **-4 is part of the solution** - **False**. The boundary -4 itself is not included in the solution (open circle).

6. **x < -4** - **False**. This is not true as we have established \(x\) must be greater than -4.

Thus, the three correct statements are:
- The graph has an open circle.
- x > -4.
- -3 is part of the solution.