Solving Simple Inequalities Using Additive and Multiplicative Inverses

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. It includes examples of solving inequalities and highlights common mistakes, such as forgetting to switch the inequality sign when necessary.

What does the addition property of equality state?

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

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

• Adding a positive number to one side of an equation makes it false.

• Adding a negative number to one side of an equation makes it false.

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

• Keep the inequality sign the same.

• Reverse the inequality sign.

• Subtract a negative number from both sides.

• Add a positive number to both sides.

In the inequality 3x < -15, what is the solution for x?

• x > -5

• x < -5

• x = -5

• x > 5

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

• Subtract 2 from both sides.

• Add 2 to both sides.

• Multiply both sides by 4.

• Divide both sides by -4.

What is a common mistake when solving inequalities involving multiplication by a negative number?

• Forgetting to reverse the inequality sign.

• Dividing both sides by a positive number.

• Forgetting to add the same number to both sides.

• Multiplying both sides by a positive number.

If -4x > 16, what should you do after multiplying both sides by -1/4?

• Keep the inequality sign the same.

• Reverse the inequality sign.

• Add 4 to both sides.

• Subtract 4 from both sides.

What is the solution for x in the inequality -4x + 2 < 14 after solving it completely?

• x > -3

• x < -3

• x < 3

• x = -3