Solving and Understanding Inequalities

This video tutorial teaches how to solve simple inequalities using additive and multiplicative inverses. It reviews the properties of equality and inequality, demonstrating how to maintain true statements when adding or multiplying both sides of an equation or inequality. The tutorial emphasizes the need to reverse the inequality sign when multiplying by a negative number. Two example inequalities are solved step-by-step, highlighting common mistakes and ensuring understanding of the concepts.

What does the addition property of equality state?

• Adding the same number to both sides of an equation keeps it true.

• Subtracting the same number from both sides of an equation makes it false.

• Adding different numbers to both sides of an equation keeps it true.

• Multiplying both sides of an equation by the same number keeps it true.

What happens when you multiply both sides of an equation by the same number?

• The equation becomes an inequality.

• The equation remains true.

• The equation becomes false.

• The equation needs to be reversed.

What is the result of adding a negative number to both sides of a true inequality?

• The inequality remains true.

• The inequality becomes an equation.

• The inequality sign needs to be reversed.

• The inequality becomes false.

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

• Add a positive number to both sides.

• Keep the inequality sign the same.

• Reverse the inequality sign.

• Subtract a negative number from both sides.

What is the solution to the inequality 3x < -15?

• x > 5

• x < 5

• x > -5

• x < -5

How do you verify the solution to an inequality?

• By checking if the solution satisfies the original inequality.

• By adding the solution to both sides of the inequality.

• By reversing the inequality sign.

• By multiplying the solution by a negative number.

What is the first step in solving the inequality -4x + 2 < 14?

• Divide both sides by -4.

• Add 2 to both sides.

• Multiply both sides by 4.

• Subtract 2 from both sides.

Why is it important to reverse the inequality sign when multiplying by a negative number?

• To convert the inequality into an equation.

• To ensure the inequality remains true.

• To simplify the inequality.

• To make the inequality false.

What is the solution to the inequality -4x + 2 < 14 after solving?

• x > 3

• x < 3

• x > -3

• x < -3

What common mistake should be avoided when solving inequalities?

• Forgetting to divide both sides by the same number.

• Forgetting to subtract the same number from both sides.

• Forgetting to reverse the inequality sign when multiplying by a negative number.

• Forgetting to add the same number to both sides.