Math Problem Statement

Which graph shows the inequality x ≥ 0?

Solution

The question asks which graph represents the inequality x0x \geq 0.

To solve this:

  • The inequality x0x \geq 0 means "all values of xx that are greater than or equal to zero."
  • On the number line, this would start at 00 and include all values to the right (positive values). Since xx can also be equal to zero, the circle at 00 should be filled in to indicate that zero is included.

Now, let's analyze the graphs:

  • The first graph has a solid dot at 00 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 00 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:

  1. What is the difference between x0x \geq 0 and x>0x > 0 on a number line?
  2. How would you graph x3x \leq 3?
  3. Can you explain the meaning of an open vs. closed circle on a number line?
  4. How do you graph a compound inequality like 3x<5-3 \leq x < 5?
  5. What happens if the inequality is x0x \neq 0? 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 \geq or \leq), 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