Question

Write an inequality using the variable x that corresponds to the set graphed on the number line.
-7
-6
-5
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-1
0
1
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5
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7
Question content area bottom
Part 1
A.
1 ​< x​ < 5
B.
1 ​< x less than or equals 5
C.
1 less than or equals x​ < 5
D.
1 less than or equals x less than or equals 5

Answer 1

To represent the set graphed on the number line that corresponds to the provided options, we need to determine the correct interval based on the descriptions given:

- **Option A**: \( 1 < x < 5 \) → This means \( x \) is strictly greater than 1 and strictly less than 5.
- **Option B**: \( 1 < x \leq 5 \) → This means \( x \) is strictly greater than 1 and less than or equal to 5.
- **Option C**: \( 1 \leq x < 5 \) → This means \( x \) is greater than or equal to 1 and strictly less than 5.
- **Option D**: \( 1 \leq x \leq 5 \) → This means \( x \) is greater than or equal to 1 and less than or equal to 5.

Assuming the graph shows an open interval at 1 (not including 1) and a closed interval at 5 (including 5), the correct inequality that describes this situation would be **Option B**:

\[ 1 < x \leq 5 \]

This indicates that \( x \) is greater than 1 and can equal 5. If the graph depicted is different, please provide additional clarification.