Understanding Inequalities

This video tutorial introduces the concept of mathematical inequalities, explaining the symbols used to compare expressions. It covers how to graph inequalities, solve them, and the special rule of reversing the inequality sign when multiplying or dividing by a negative number. The tutorial includes examples and step-by-step solutions to help viewers understand the process of solving and graphing inequalities.

What is an inequality in mathematics?

• A statement that only uses numbers

• A statement that shows equality between two expressions

• A statement that involves only addition and subtraction

• A statement that compares two expressions using symbols

Which symbol represents 'less than'?

• ≠

• >

• <

• =

How do you graph an inequality that is 'less than'?

• Using a closed circle

• Using an open circle

• Using a square

• Using a triangle

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

• Subtract a positive number from both sides

• Add a positive number to both sides

• Reverse the direction of the inequality sign

• Keep the inequality sign the same

In the example where 'a' is less than 6, what type of circle is used on the number line?

• Square

• Open circle

• Triangle

• Closed circle

What is the result of dividing 90 by 15 in the first example?

• 8

• 7

• 6

• 5

When solving the second example, what is the first step after applying the distributive property?

• Add a constant to both sides

• Subtract a constant from both sides

• Divide by a positive number

• Combine like terms

What is the final inequality solution in the second example?

• x is less than or equal to -7

• x is less than or equal to 7

• x is greater than or equal to -7

• x is greater than or equal to 7

Why do we flip the inequality sign in the second example?

• Because we added a positive number

• Because we multiplied by a positive number

• Because we subtracted a positive number

• Because we divided by a negative number

What type of circle is used on the number line for the solution in the second example?

• Square

• Open circle

• Triangle

• Closed circle