Understanding Inequalities and Operations

The video tutorial explains how to solve an inequality involving the variable w. It demonstrates the process of isolating w by undoing division with multiplication and highlights the importance of changing the direction of the inequality sign when multiplying or dividing by a negative number. The tutorial emphasizes that this change is only necessary with multiplication or division by negatives, not with addition or subtraction.

What is the first step in solving an inequality for a variable?

• Add a constant to both sides

• Subtract a constant from both sides

• Multiply both sides by zero

• Isolate the variable on one side

What is the main focus of the video tutorial?

• Calculating derivatives

• Solving equations

• Solving inequalities

• Graphing functions

When isolating a variable, what operation can undo division?

• Addition

• Subtraction

• Multiplication

• Division

What operation is used to isolate 'w' in the inequality?

• Division

• Subtraction

• Addition

• Multiplication

If 'w' is divided by -4, what should you multiply both sides by to isolate 'w'?

• -4

• -5

• 4

• 5

What is the result of multiplying -5 by -4?

• 9

• -9

• 20

• -20

What is the result of multiplying a negative by a negative?

• Zero

• A positive

• A negative

• Undefined

What is the result of multiplying -5 by 4?

• -20

• 20

• -9

• 9

What happens to the inequality sign when you multiply both sides by a negative number?

• It stays the same

• It becomes an equal sign

• It changes direction

• It disappears

Why do we need to change the direction of the inequality sign when multiplying by a negative?

• To avoid division by zero

• To make the equation easier

• To maintain the inequality's truth

• Because it is a rule for all operations