Math Problem Statement

x > −2

Solution

The inequality x>2x > -2 describes the set of all real numbers greater than 2-2. This can be represented in various forms:

1. Number Line Representation

  • On a number line, the solution is all points to the right of 2-2, with an open circle at 2-2 indicating that 2-2 is not included.

2. Interval Notation

  • The solution is written as (2,)(-2, \infty), meaning all numbers greater than 2-2 but not including 2-2.

3. Graphical Interpretation

  • If you graph it in the Cartesian plane, the solution is a vertical strip where x>2x > -2.

4. Real-Life Example

  • This inequality could represent a scenario like temperatures higher than 2-2 degrees Celsius.

Would you like to explore this concept further or discuss its application in a specific context?


Here are 5 related questions to deepen your understanding:

  1. How would the inequality x2x \geq -2 differ from x>2x > -2?
  2. What is the solution set for x>2x > -2 if xx is restricted to integers?
  3. How can you represent the inequality x>2x > -2 as an equation for boundary conditions?
  4. How would x>2x > -2 change if the inequality were reversed to x<2x < -2?
  5. What happens to the solution if you square both sides of x>2x > -2?

Tip: Always double-check the boundary conditions when solving inequalities; small changes in the sign (>>, \geq) can alter the solution significantly.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

-

Theorems

Properties of inequalities

Suitable Grade Level

Grades 6-8