Solving Inequalities: Multiplication and Division Techniques

This video tutorial introduces the concept of inequalities, explaining how they differ from equalities. It covers solving inequalities using multiplication and division, similar to solving one-step equations but with an inequality sign. The tutorial demonstrates the multiplication and division properties of inequalities, emphasizing the need to perform operations on both sides to maintain truth. Two examples are provided: solving 8X ≤ 40 and D/2 > 7, with detailed steps to find the solutions.

What is the main focus of this lesson?

• Understanding equalities

• Solving equations by addition or subtraction

• Solving inequalities by multiplication or division

• Graphing linear equations

What is an inequality?

• A comparison between two quantities that are not equal

• A statement that two quantities are equal

• A type of graph

• A method to solve equations

What must you do if you multiply a number on one side of an inequality?

• Multiply a different number on the other side

• Multiply the same number on the other side

• Add the same number on the other side

• Divide the same number on the other side

What is the purpose of the multiplication and division properties in inequalities?

• To keep the inequality true

• To make the quantities equal

• To simplify the equation

• To change the inequality sign

In the example 8X ≤ 40, what operation is used to solve for X?

• Multiplication

• Subtraction

• Division

• Addition

What is the solution to the inequality 8X ≤ 40?

• X > 5

• X < 5

• X ≥ 5

• X ≤ 5

What is the opposite operation of multiplication?

• Addition

• Division

• Exponentiation

• Subtraction

In the example D/2 > 7, what operation is used to solve for D?

• Multiplication

• Addition

• Subtraction

• Division

What is the solution to the inequality D/2 > 7?

• D ≤ 14

• D > 14

• D < 14

• D ≥ 14

What should you not forget to do when solving inequalities?

• Add the same number on both sides

• Multiply by zero

• Draw your lines

• Change the inequality sign