QQuestionMathematics
QuestionMathematics
Which graph represents the compound inequality −3<n<1?
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Answer
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Step 1:I'll solve this step by step, following the LaTeX formatting guidelines precisely.
Step 2:: Understand the Compound Inequality
The compound inequality $$-3 < n < 1$$ means that n is greater than -3 AND less than 1.
This represents all real numbers between - 3 and 1, excluding the endpoints.
Step 3:: Visualize the Inequality on a Number Line
- The left boundary is - 3 (exclusive) - The right boundary is 1 (exclusive) - This creates an open interval between - 3 and 1
Step 4:: Interpret the Graph
We need to look for a graph that: - Has an open circle (hollow dot) at - 3 - Has an open circle (hollow dot) at 1 - Shows a solid line segment connecting these points - Indicates all points between these two values
Step 5:: Identify the Correct Graph
The graph that matches these characteristics will have: - A hollow dot at - 3 on the left side - A hollow dot at 1 on the right side - A solid line segment between these points - Arrows pointing to the open dots to show the interval continues
Final Answer
The graph representing - 3 < n < 1 is the graph with an open interval between - 3 and 1.
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