Solving Linear Inequalities in Algebra 2

The video tutorial covers systems of inequalities, starting with an introduction to inequalities and their symbols. It explains how to graph inequalities, emphasizing the importance of solving for y and using slope-intercept form. The tutorial includes multiple examples, demonstrating how to solve and graph inequalities, identify solution sets, and understand parallel lines. It also discusses scenarios where no solution exists. The video concludes with a review of key concepts and encourages students to practice and test their understanding.

What is the first step in solving the inequality 2y < -3x + 4?

• Add 3x to both sides

• Subtract 3x from both sides

• Multiply both sides by 2

• Divide both sides by 2

When graphing the inequality y < -3/2x + 2, what type of line should be used?

• Bold line

• Dashed line

• Dotted line

• Solid line

If y is less than a given line, where should the shading be done?

• To the left of the line

• On the line

• Below the line

• Above the line

What does a solid line indicate when graphing an inequality?

• The line is not part of the solution

• The inequality is strict

• The inequality is not strict

• The line is part of the solution

In the inequality -2y < x - 4, what happens when you divide by -2?

• The inequality becomes an equation

• The inequality sign switches direction

• The inequality sign is removed

• The inequality sign remains the same

What is the slope of the line y > -1/2x + 2?

• -1/2

• 2

• -2

• 1/2

When graphing y > -1/2x + 2, where should the shading be done?

• Above the line

• Below the line

• On the line

• To the left of the line

What type of line is used for the inequality y > -x + 3?

• Dashed line

• Solid line

• Dotted line

• Bold line

What is the solution set for two parallel lines with no intersection?

• All points on the graph

• No solution

• Only the points on the lines

• Only the points between the lines

Is the point (2, 3) a solution for the system x ≥ 0 and y > 5/2x - 2?

• Yes, it is in the solution set

• No, it is not in the solution set

• Yes, it is on the boundary

• No, it is outside the graph