Math Problem Statement
Which graph shows the inequality x ≥ 0?
Solution
The question asks which graph represents the inequality .
To solve this:
- The inequality means "all values of that are greater than or equal to zero."
- On the number line, this would start at and include all values to the right (positive values). Since can also be equal to zero, the circle at should be filled in to indicate that zero is included.
Now, let's analyze the graphs:
- The first graph has a solid dot at and an arrow pointing to the right, representing values greater than or equal to zero. This matches the inequality.
- The other graphs either have an open circle at or arrows pointing in the wrong direction, which does not satisfy the inequality.
Thus, the first graph is the correct one.
Would you like more details or have any questions?
Here are 5 related questions to expand on this:
- What is the difference between and on a number line?
- How would you graph ?
- Can you explain the meaning of an open vs. closed circle on a number line?
- How do you graph a compound inequality like ?
- What happens if the inequality is ? How would it be graphed?
Tip: When working with inequalities, always pay attention to whether the inequality is strict (using or ) or includes equality (using or ), as this changes how you represent the boundary points on a graph.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Number Line Representation
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8