Math Problem Statement

Graph the solution set of the inequality, where x is a real number, on the number line. x ≥ 14

Solution

The inequality given is:

x14x \geq 14

This means that xx can be any number greater than or equal to 14.

To graph this on the number line:

  • There should be a solid dot at 14 (because xx is equal to 14).
  • The line should extend to the right (towards greater values) since xx is also greater than 14.

The correct graph will show a solid dot at 14 with a line extending to the right.

Looking at the options:

  • Option D shows the correct graph: a solid dot at 14 and the arrow going to the right, indicating values greater than or equal to 14.

So, the correct answer is Option D.

If you have more questions or need further clarification, feel free to ask!

Here are some related questions you might find useful:

  1. How would the graph change if the inequality was x>14x > 14?
  2. What would the graph look like for x14x \leq 14?
  3. How would you represent x<14x < 14 on the number line?
  4. Can xx be a fraction in the solution for x14x \geq 14?
  5. How do you represent x=14x = 14 only on a number line?

Tip: Always use a solid dot for "greater than or equal to" (\geq) or "less than or equal to" (\leq), and an open circle for strict inequalities (>> or <<).

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Math Problem Analysis

Mathematical Concepts

Inequalities
Number Line Representation

Formulas

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Theorems

Inequality Representation Theorem

Suitable Grade Level

Grades 6-8