The point which doesn't satisfy the inequality : 3x - 2y >= -6 is:
(2 Points)

 

(1,2)

(-2,3)

(2,3)

(2,1)

We are given the inequality \( 3x - 2y \geq -6 \) and need to determine which point does not satisfy the inequality from the options provided.

Let's substitute the coordinates of each point into the inequality.

1. **For \( (1, 2) \):**
   \[
   3(1) - 2(2) = 3 - 4 = -1
   \]
   \[
   -1 \geq -6 \quad \text{(True)}
   \]

2. **For \( (-2, 3) \):**
   \[
   3(-2) - 2(3) = -6 - 6 = -12
   \]
   \[
   -12 \geq -6 \quad \text{(False)}
   \]

3. **For \( (2, 3) \):**
   \[
   3(2) - 2(3) = 6 - 6 = 0
   \]
   \[
   0 \geq -6 \quad \text{(True)}
   \]

4. **For \( (2, 1) \):**
   \[
   3(2) - 2(1) = 6 - 2 = 4
   \]
   \[
   4 \geq -6 \quad \text{(True)}
   \]

The point that **does not satisfy** the inequality is **(-2, 3)**.

### Do you need more details or have any questions? 

Here are some related questions for you:

1. What happens if the inequality were strict, like \( 3x - 2y > -6 \)?
2. How would the solution change if the inequality had been \( 3x + 2y \geq -6 \)?
3. Can you plot the line \( 3x - 2y = -6 \) and shade the solution region?
4. What would happen if the inequality were reversed, \( 3x - 2y \leq -6 \)?
5. How can inequalities be represented in 3-dimensional space?

**Tip:** To check if a point satisfies an inequality, always substitute the coordinates directly into the inequality and verify the truth of the statement.

The point which doesn't satisfy the inequality : 3x - 2y >= -6 is:
(1,2)
(-2,3)
(2,3)
(2,1)

Determine which point does not satisfy the inequality 3x - 2y >= -6 using a step-by-step substitution approach. This problem introduces key concepts in algebra and inequalities, suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation