Question

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

A. X <-4
B. The graph has an open circle.
C. x > -4
D. -4 is part of the solution
E. -3 is part of the solution
F. The graph has a closed circle.

Answer 1

To solve the inequality \(10 < 14 + x\), we can start by isolating \(x\):

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

So, we can now evaluate the statements based on this solution:

A. **X <-4** - **False**: This statement suggests that \(x\) is less than -4, which is incorrect since we found \(x > -4\).

B. **The graph has an open circle.** - **True**: Since the inequality is strict (greater than), the graph will have an open circle at -4.

C. **x > -4** - **True**: This is one of the results we derived from solving the inequality.

D. **-4 is part of the solution** - **False**: Since \(x\) must be greater than -4, -4 itself is not part of the solution set.

E. **-3 is part of the solution** - **True**: Since -3 is greater than -4, it is indeed part of the solution.

F. **The graph has a closed circle.** - **False**: The graph will not have a closed circle because -4 is not included in the solution.

Based on this analysis, the three correct answers are:

**B, C, E.**