Solving Inequalities: Key Concepts and Techniques

This video tutorial covers solving inequalities using multiplication and division. It explains the properties of inequalities when multiplying or dividing by positive and negative numbers. The tutorial emphasizes the importance of switching the inequality sign when dealing with negative numbers. It includes practice problems to reinforce the concepts taught.

Result of multiplying both sides of an inequality by the same positive number?

• None of the above.

• Inequality becomes an equation.

• Inequality remains unchanged.

• Inequality sign switches direction.

Outcome of dividing both sides of an inequality by a positive number?

• Result is always positive.

• Result is always negative.

• Inequality sign remains the same.

• Inequality sign reverses.

When multiplying/dividing an inequality by a negative number, what must you do?

• Keep the inequality sign the same.

• Switch the inequality sign.

• Convert the inequality to an equation.

• Multiply or divide by 2.

Result of dividing both sides of an inequality by a negative number?

• Inequality sign flips.

• Inequality sign stays the same.

• Inequality becomes a positive number.

• Inequality becomes a negative number.

-3 is less than 4, both sides multiplied by -2, new relationship?

• -6 is greater than 8.

• -6 is less than 8.

• 6 is greater than -8.

• 6 is less than -8.

Importance of switching inequality sign when multiplying/dividing by a negative number?

• To simplify the inequality further.

• Fundamental rule of algebra.

• To correctly reflect the relationship between the numbers.

• To maintain the inequality's original value.

Solving -5x > 15 requires dividing by which number?

• 15

• -5

• 5

• -15

After dividing -5x > 15 by -5, new inequality?

• x > -3

• x < 3

• x < -3

• x > 3

Correct step to isolate x in x/-2 > 5/2?

• Divide both sides by 2.

• Multiply both sides by 2.

• Multiply both sides by -2.

• Divide both sides by -2.

Solution to x/-2 > 5/2 after isolating x?

• x < -5

• x > -5

• x < 5

• x > 5