Solving Linear Inequalities: Rules and Examples

The video tutorial explains how to solve linear inequalities, emphasizing that the process is similar to solving linear equations. Key points include maintaining the direction of the inequality sign and flipping it when multiplying or dividing by a negative number. Several examples are provided to illustrate these concepts, including solving simple inequalities and combined inequalities. The tutorial concludes with a summary of the main rules and nuances to remember when dealing with inequalities.

What is the key similarity between solving linear equations and inequalities?

• You only need to solve one side.

• You can ignore the inequality sign.

• Only addition and subtraction are allowed.

• Operations must be performed on both sides.

In the inequality 3x > 9, what is the value of x?

• x = 3

• x > 9

• x < 3

• x > 3

When solving x + 5 ≤ 16, what operation is performed to isolate x?

• Add 5 to both sides

• Divide both sides by 5

• Subtract 5 from both sides

• Multiply both sides by 5

What must you do when you swap the sides of an inequality?

• Multiply by a negative number

• Add a constant to both sides

• Nothing, just swap them

• Flip the inequality sign

Why is it necessary to flip the inequality sign when dividing by a negative number?

• To ensure the solution is correct

• To make the equation easier

• To keep the inequality balanced

• To simplify the inequality

In the inequality -2x > 4, what is the solution for x?

• x < -2

• x > -2

• x < 2

• x > 2

How do you solve combined inequalities like 4 < 3x + 1 < 16?

• Ignore the middle term

• Only solve the first inequality

• Solve each part separately

• Solve them as a single equation

What is the solution for the inequality 3x + 2 > 11?

• x > 3

• x > 2

• x < 3

• x = 3

What is the range of x in the inequality 1 < x < 5?

• x is less than 1

• x is greater than 5

• x is between 1 and 5

• x is equal to 3

What are the two main rules to remember when solving inequalities?

• Solve them like equations without any changes

• Only use addition and subtraction

• Keep the sign direction and flip it when multiplying/dividing by a negative

• Always add a constant and ignore the sign