Question

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

A. The graph has an open circle.
B. x ≤ - 12
C. -13 is part of the solution
D. x ≥ - 12
E. -11 is part of the solution
F. The graph has a close circle.

Answer 1

To solve the inequality \(10 ≥ 22 + x\), we start by isolating \(x\):

1. Subtract \(22\) from both sides:
\[
10 - 22 ≥ x
\]
which simplifies to
\[
-12 ≥ x
\]
or
\[
x ≤ -12
\]

From this solution, we can analyze the statements provided:

A. The graph has an open circle. **(False)** - Since the inequality is \(≤\), it includes -12, which means there would be a closed circle.

B. \(x ≤ -12\) **(True)** - This directly matches our solution.

C. -13 is part of the solution **(True)** - Since -13 is less than -12, it satisfies the inequality \(x ≤ -12\).

D. \(x ≥ -12\) **(False)** - The solution indicates that \(x\) must be less than or equal to -12, not greater than or equal.

E. -11 is part of the solution **(False)** - -11 is greater than -12, therefore does not satisfy \(x ≤ -12\).

F. The graph has a closed circle. **(True)** - As previously noted, since the inequality is \(≤\), we would graph a closed circle at -12.

### Summary of correct answers:
- B. \(x ≤ -12\)
- C. -13 is part of the solution
- F. The graph has a closed circle.