Exploring Solutions to Linear Inequalities

The video tutorial covers linear inequalities, explaining how they differ from linear equations by using inequality symbols instead of equal signs. It discusses how to determine if an ordered pair is a solution to a linear inequality algebraically. The tutorial then moves on to graphing linear inequalities on a coordinate plane, explaining the use of solid or dotted lines based on the inequality symbol and how to shade the solution area. Several examples are provided to illustrate these concepts, including solving inequalities for y and graphing them, with a focus on understanding the solution set visually and algebraically.

What is a linear inequality?

• An equation with an equal sign

• An equation with an inequality symbol

• A polynomial equation

• A quadratic equation

Which of the following is NOT an inequality symbol?

• <

• ≤

• =

• >

How do you determine if an ordered pair is a solution to a linear inequality?

• By graphing the inequality

• By substituting the values into the inequality

• By solving for x

• By solving for y

What is the result of substituting (3, 9) into the inequality 9 ≥ 15 - 6?

• Undefined

• True

• False

• Cannot be determined

When graphing a linear inequality, what does a dotted line represent?

• The inequality is a quadratic

• The inequality is undefined

• The inequality does not include the boundary line

• The inequality includes the boundary line

In the inequality y > 2x - 4, where should you shade on the graph?

• To the left of the line

• Above the line

• Below the line

• On the line

What is the first step in graphing a linear inequality?

• Find the x-intercept

• Draw the axes

• Convert to slope-intercept form

• Shade the region

For the inequality y ≤ -1/2x + 1, what type of line should be drawn?

• Dotted

• None

• Solid

• Dashed

If the inequality is y > -3, where should you shade?

• To the left of the line

• On the line

• Below the line

• Above the line

For the inequality x ≤ 3, what type of line should be drawn?

• None

• Dashed

• Solid

• Dotted