Math Problem Statement

Which of the following options matches the inequality x > 2?

Solution

The question in the image asks you to identify the correct set notation for the inequality x>2x > 2.

In interval notation:

  • x>2x > 2 represents all values greater than 2, but not including 2 itself.
  • In interval notation, this is written as x]2,[x \in ]2, \infty[, which means that xx belongs to the open interval from 2 (exclusive) to infinity.

Now let's analyze the options:

  1. x[2.01;[x \in [2.01; \infty[: This starts at 2.01, which is slightly more than 2. It excludes 2 but starts at a higher value, so it does not match.
  2. x]2;[x \in ]2; \infty[: This correctly represents the inequality x>2x > 2 because it excludes 2 and goes to infinity.

Thus, the correct answer is the second option: x]2;[x \in ]2; \infty[.

Would you like more details on interval notation or inequalities? Here are some related questions to expand on:

  1. What is the difference between open and closed intervals?
  2. How would you represent x2x \geq 2 in interval notation?
  3. Can you explain how infinity works in interval notation?
  4. How do you solve inequalities with both upper and lower bounds?
  5. How can inequalities be visualized on a number line?

Tip: Always check whether the inequality includes or excludes the boundary value when translating it into interval notation!

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Math Problem Analysis

Mathematical Concepts

Inequalities
Interval Notation

Formulas

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Theorems

Basic properties of inequalities

Suitable Grade Level

Grades 7-9