Understanding Graphical Solutions of Inequalities

The video tutorial explains how to determine solutions for inequalities using graphs. It covers two types of inequalities: those with solid lines, indicating solutions include points on the line, and those with dashed lines, indicating solutions do not include points on the line. The tutorial provides examples of each type, showing how to identify solutions within shaded regions and verify them through substitution.

What is the inequality we are trying to solve using the graph?

• x + y < 4

• x - y > 4

• x + 2y ≤ 4

• x - 2y ≥ 4

Why is the line in the graph solid?

• Because the line is not part of the solution

• Because the inequality includes 'or equal to'

• Because the inequality is less than

• Because the inequality is strict

Which of the following ordered pairs is a solution to the inequality x - 2y ≥ 4?

• (6, 5)

• (-3, -3)

• (2, -1)

• (3, 5)

Which ordered pair is a solution for the inequality x - 2y ≥ 4?

• (-3, -3)

• (4, -3)

• (3, 5)

• (0, 0)

What does a dashed line in a graph of an inequality indicate?

• The line is part of the solution

• The line is not related to the inequality

• The inequality is strict and does not include 'or equal to'

• The inequality is less than or equal to

For the inequality x + y > 2, which of the following points is a solution?

• (-1, 4)

• (4, -1)

• (2, 0)

• (0, 2)

Which point is not a solution for the inequality x + y > 2?

• (4, -1)

• (4, 4)

• (-1, 4)

• (6, -5)

Which of the following is true about the inequality x + y > 2?

• The line is not part of the graph

• The line is both solid and dashed

• The line is dashed

• The line is solid

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

• It represents the non-solutions

• It is unrelated to the inequality

• It represents the solutions

• It only includes points on the line

What should you do to verify if an ordered pair satisfies an inequality?

• Perform substitution into the inequality

• See if it is in the shaded region

• Check if it lies on the line

• Compare it with other ordered pairs