Write an inequality using the variable x that corresponds to the set graphed on the number line.

Question

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Part 1
A.
2 less than or equals x​ < 6
B.
2 less than or equals x less than or equals 6
C.
2 ​< x​ < 6
D.
2 ​< x less than or equals 6

Answer 1

To determine the correct inequality, we need to identify how the set is graphed on the number line. Since you haven't provided a specific visual, I will explain how to interpret the options.

1. Option A: \(2 \leq x < 6\) - This means that \(x\) can be equal to 2 but cannot reach 6. The interval includes 2 and everything up to but not including 6.

2. Option B: \(2 \leq x \leq 6\) - This means that \(x\) can include both 2 and 6. The interval ranges from 2 to 6, inclusive of both endpoints.

3. Option C: \(2 < x < 6\) - This means that \(x\) can be any value greater than 2 but less than 6. The endpoints 2 and 6 are not included.

4. Option D: \(2 < x \leq 6\) - This signifies that \(x\) can be any value greater than 2 but can be equal to 6. The interval includes 6 but not 2.

Now, depending on how the number line appears relative to these intervals, you should select the appropriate option. Here’s a quick summary:

• If the interval starts from 2 (including) and ends at 6 (excluding), choose A.
• If both 2 and 6 are included, choose B.
• For an open interval between 2 and 6 (neither included), go with C.
• If 2 is not included but 6 is, choose D.

If you can clarify how it's graphed or provide the boundaries, I can help you select the correct inequality.