https://file.aiquickdraw.com/mathbot/file/1726843265370bjft8v4a.jpg

The problem asks to determine which point among the given options satisfies the inequality \( x > 3y - 2 \).

The options provided are:
- (2, 3)
- (5, 0)
- (-2, 0)
- (-2, 5)

We will check each point to see if it satisfies the inequality.

1. For (2, 3):
   \[
   x = 2, \quad y = 3
   \]
   Check if:
   \[
   2 > 3(3) - 2
   \]
   \[
   2 > 9 - 2
   \]
   \[
   2 > 7 \quad \text{(False)}
   \]
   So, (2, 3) is **not** a solution.

2. For (5, 0):
   \[
   x = 5, \quad y = 0
   \]
   Check if:
   \[
   5 > 3(0) - 2
   \]
   \[
   5 > 0 - 2
   \]
   \[
   5 > -2 \quad \text{(True)}
   \]
   So, (5, 0) **is** a solution.

3. For (-2, 0):
   \[
   x = -2, \quad y = 0
   \]
   Check if:
   \[
   -2 > 3(0) - 2
   \]
   \[
   -2 > 0 - 2
   \]
   \[
   -2 > -2 \quad \text{(False)}
   \]
   So, (-2, 0) is **not** a solution.

4. For (-2, 5):
   \[
   x = -2, \quad y = 5
   \]
   Check if:
   \[
   -2 > 3(5) - 2
   \]
   \[
   -2 > 15 - 2
   \]
   \[
   -2 > 13 \quad \text{(False)}
   \]
   So, (-2, 5) is **not** a solution.

### Conclusion:
The correct solution is **(5, 0)**.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:
1. How do you solve inequalities involving two variables?
2. What is the geometric representation of inequalities like \(x > 3y - 2\)?
3. Can a point satisfy more than one inequality?
4. How do systems of inequalities work?
5. What happens when you reverse the inequality sign?

**Tip:** When solving inequalities, always test each point by substituting the coordinates into the inequality to check if it holds true.

Which among the following is a solution of x > 3y - 2?

Learn how to solve the inequality x > 3y - 2 with detailed step-by-step solutions. This problem involves checking given points to determine which satisfies the inequality. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation