Understanding Inequalities with Ordered Pairs

The video tutorial explains how to determine if ordered pairs satisfy the inequality 3x - 2y > 12. It demonstrates this through three examples, substituting values into the inequality and checking if the result is true or false. The tutorial also includes a graphical representation, showing which points satisfy the inequality and explaining the significance of dashed versus solid lines. The video aims to help students understand the process of testing ordered pairs against inequalities and interpreting graphical data.

What is the first step in determining if an ordered pair satisfies the inequality 3x - 2y > 12?

• Graph the inequality

• Check if x is greater than y

• Substitute the x and y values into the inequality

• Solve for y

In the first example, what is the result of substituting x = -2 and y = 1 into the inequality?

• 8 < 12, which is false

• 8 > 12, which is true

• -8 > 12, which is false

• -8 < 12, which is true

What conclusion can be drawn from the first example?

• The ordered pair is irrelevant

• The ordered pair is on the boundary

• The ordered pair does not satisfy the inequality

• The ordered pair satisfies the inequality

In the second example, what is the result of substituting x = 5 and y = -2 into the inequality?

• 19 > 12, which is true

• 19 < 12, which is false

• 15 > 12, which is true

• 15 < 12, which is false

What conclusion can be drawn from the second example?

• The ordered pair is on the boundary

• The ordered pair does not satisfy the inequality

• The ordered pair satisfies the inequality

• The ordered pair is irrelevant

In the third example, what is the result of substituting x = 2 and y = -3 into the inequality?

• 12 = 12, which is true

• 12 > 12, which is false

• 12 < 12, which is true

• 12 = 12, which is false

What conclusion can be drawn from the third example?

• The ordered pair is irrelevant

• The ordered pair does not satisfy the inequality

• The ordered pair satisfies the inequality

• The ordered pair is on the boundary

What does a dashed line represent in the graphical representation of the inequality?

• The inequality is undefined

• Points on the line do not satisfy the inequality

• Points on the line satisfy the inequality

• The inequality is equal

How would the inequality change if the line were solid instead of dashed?

• Points on the line would still not satisfy the inequality

• Points on the line would satisfy the inequality

• The inequality would become undefined

• The inequality would become less than

What is the significance of the shaded region in the graph of the inequality?

• It represents points that are equal

• It represents points that are irrelevant

• It represents points that do not satisfy the inequality

• It represents points that satisfy the inequality