Solving Linear Inequalities and Interval Notation

This video tutorial covers the basics of solving linear inequalities in one variable. It begins with an introduction to inequality symbols and types, including strict and non-strict inequalities. The tutorial then explains how to graph inequalities on a number line using interval notation. Key properties of inequalities, such as the addition and multiplication properties, are discussed. The video concludes with step-by-step examples of solving linear inequalities, emphasizing the importance of flipping the inequality sign when multiplying or dividing by a negative number.

Which symbol represents a strict inequality where one value is less than another?

• ≤

• <

• ≥

• =

What does the symbol '≥' represent?

• Less than

• Greater than

• Equal to

• Greater than or equal to

How do you graph the inequality x > 2 on a number line?

• A filled dot at 2 and shading to the right

• An open circle at 2 and shading to the right

• A filled dot at 2 and shading to the left

• An open circle at 2 and shading to the left

In interval notation, how is the solution to x > 2 represented?

• [2, ∞]

• (2, ∞)

• (2, ∞]

• [2, ∞)

What does a bracket in interval notation indicate?

• The number is not included

• The number is included

• The interval is infinite

• The interval is finite

How do you graph the inequality x ≤ 5 using a filled dot or circle?

• An open circle at 5 and shading to the right

• A filled dot at 5 and shading to the right

• An open circle at 5 and shading to the left

• A filled dot at 5 and shading to the left

What is the addition property of inequality?

• You can multiply or divide both sides by the same negative number without changing the solution

• You can add or subtract the same number from both sides without changing the solution

• You can multiply or divide both sides by the same positive number without changing the solution

• You can add or subtract different numbers from both sides without changing the solution

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Keep the inequality the same

• Add the same number to both sides

• Subtract the same number from both sides

• Reverse the direction of the inequality

What is the solution to the inequality 7x < 28?

• x ≥ 4

• x < 4

• x > 4

• x ≤ 4

How do you represent the solution to x ≤ -6 in interval notation?

• (-∞, -6]

• (-∞, -6)

• [-∞, -6)

• [-∞, -6]