Question

Which of the following are solutions to the inequality below? Select all that apply.

2 ≤
x
− 9
X=9x=12x=11x=10

Answer 1

To solve the inequality \( 2 \leq x - 9 \), we first isolate \( x \) on one side:

1. Add 9 to both sides:
\[
2 + 9 \leq x
\]
\[
11 \leq x
\]
or equivalently,
\[
x \geq 11
\]

Now, we evaluate the given options:
- \( x = 9 \) (does not satisfy \( x \geq 11 \))
- \( x = 10 \) (does not satisfy \( x \geq 11 \))
- \( x = 11 \) (satisfies \( x \geq 11 \))
- \( x = 12 \) (satisfies \( x \geq 11 \))

The solutions to the inequality are:
- \( x = 11 \)
- \( x = 12 \)

So, the correct answers are \( x = 11 \) and \( x = 12 \).