Understanding Graphical Solutions of Inequalities

The video tutorial explains how to determine ordered pairs of solutions from graphs. It covers two examples: one with a solid boundary line indicating solutions include points on the line and in the shaded region, and another with a dashed boundary line where solutions are only in the shaded region. The tutorial highlights the importance of understanding inequalities and their graphical representations.

What does a solid boundary line in a graph of an inequality indicate?

• The points on the line are not part of the solution.

• The points on the line are part of the solution.

• The inequality is strict.

• The inequality has no solution.

Which of the following ordered pairs is a solution in the shaded region for the inequality Y ≤ x + 1?

• (0, -1)

• (1, 1)

• (-2, 0)

• (3, 3)

For the inequality Y ≤ x + 1, which ordered pair lies on the boundary line?

• (2, -3)

• (-1, 2)

• (4, 1)

• (0, 0)

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

• The inequality has no shaded region.

• The points on the line are not part of the solution.

• The inequality is less than or equal to.

• The points on the line are part of the solution.

Which inequality is represented by a dashed boundary line?

• Y ≥ 2x - 3

• Y ≤ x + 1

• Y = x - 2

• Y > -2x + 3

For the inequality Y > -2x + 3, which ordered pair is a solution in the shaded region?

• (1, 3)

• (2, -1)

• (4, 2)

• (0, 0)

In the context of inequalities, what does the shaded region represent?

• The area where only boundary solutions exist.

• The area where all solutions exist.

• The area where no solutions exist.

• The area where solutions are not allowed.