Inequalities and Their Solutions

This tutorial explains how to solve inequalities using multiplication and division. It covers the rules for solving inequalities with both positive and negative numbers, emphasizing the need to switch the inequality sign when dealing with negative numbers. The tutorial also includes a practical example of applying these concepts to a word problem involving movie tickets.

What is the first step when solving an inequality by multiplying or dividing by a positive number?

• Switch the inequality sign

• Add a constant to both sides

• Multiply or divide both sides by the same positive number

• Subtract a constant from both sides

If 3x < 24, what is the value of x?

• x = 8

• x > 8

• x < 8

• x ≤ 8

When solving x/4 ≥ 2, what operation should be performed?

• Multiply both sides by 4

• Divide both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

What happens to the inequality sign when you multiply or divide by a negative number?

• It stays the same

• It becomes a positive sign

• It becomes an equal sign

• It reverses direction

Solve the inequality: -2x > 16.

• x > 8

• x < -8

• x > -8

• x < 8

If x/-2 < 8, what is the solution for x?

• x ≤ -16

• x = -16

• x > -16

• x < -16

What is the first step in solving -2x > 16?

• Add 2 to both sides

• Subtract 2 from both sides

• Multiply both sides by -2

• Divide both sides by -2

What is the result of multiplying both sides of x/-2 < 8 by -2?

• x < -16

• x > -16

• x = -16

• x ≤ -16

Why do we reverse the inequality sign when dividing by a negative number?

• To make the equation easier to solve

• To simplify the inequality

• To convert the inequality into an equation

• To ensure the inequality remains true

What is the result of dividing both sides of -3x < 9 by -3 without switching the inequality sign?

• x = -3

• x > -3

• x ≤ -3

• x < -3