Understanding Inequalities with Negative Variables and Fractions

This video tutorial from MooMoo Math and Science covers solving inequalities, focusing on special cases involving negative variables and negative fractions. The instructor demonstrates step-by-step methods to isolate variables and solve inequalities, emphasizing the importance of flipping the inequality sign when dividing by a negative number. The video includes three examples, each illustrating different scenarios and techniques for solving inequalities. The tutorial concludes with a reminder to practice kindness.

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

• Add a positive number to both sides

• Divide both sides by a positive number

• Subtract a positive number from both sides

• Multiply both sides by a positive number

When dividing both sides of an inequality by a negative number, what must you remember to do?

• Subtract the same number from both sides

• Add the same number to both sides

• Keep the inequality sign the same

• Flip the inequality sign

What is the purpose of putting a '1' in front of a negative variable?

• To eliminate the variable

• To simplify the equation

• To clarify the coefficient

• To make it positive

Why is it important to keep the sign of the larger number when simplifying inequalities?

• To ensure the inequality is correct

• To make the equation easier to solve

• To avoid errors in calculation

• To maintain the balance of the equation

In the context of inequalities, what does 'isolating the variable' mean?

• Adding the variable to both sides

• Subtracting the variable from both sides

• Multiplying the variable by a constant

• Getting the variable alone on one side

In the example with a negative fraction, what operation is used to isolate the variable?

• Addition

• Division by the reciprocal

• Subtraction

• Multiplication by the reciprocal

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

• It becomes a less than sign

• It becomes an equal sign

• It flips

• It stays the same

What is the result of multiplying a positive number by a negative reciprocal in an inequality?

• A negative number

• Zero

• A positive number

• An undefined number

In the final example, what is the result of dividing both sides by a negative number?

• The variable becomes positive

• The inequality sign stays the same

• The variable becomes zero

• The inequality sign flips

What is the final value of the variable in the last example after solving the inequality?

• -19

• 19

• -13

• 13