Exploring Inequalities and Their Solutions

The video tutorial explains how to solve inequalities, which are similar to equations but involve symbols like greater than or less than. The key difference is that when multiplying or dividing both sides by a negative number, the inequality sign must be flipped. The tutorial provides examples to illustrate this concept, showing step-by-step solutions and emphasizing the importance of flipping the sign when necessary.

What is an inequality?

• A mathematical statement that shows the equality of two expressions.

• A mathematical statement that shows one side is greater or less than the other.

• A formula used to calculate the area of a shape.

• A method for dividing numbers.

What symbol is not used in inequalities?

• =

• >

• ≤

• <

If 2x + 5 < 9, what is the first step to solve the inequality?

• Subtract 5 from both sides

• Add 5 to both sides

• Multiply both sides by 2

• Divide both sides by 2

After subtracting 5 from both sides in 2x + 5 < 9, what is the inequality?

• 2x ≤ 4

• 2x = 4

• 2x > 4

• 2x < 4

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Subtract 1 from both sides

• Add 1 to both sides

• Do nothing

• Flip the inequality sign

When solving -3x ≥ 21, why do we flip the inequality sign after dividing by -3?

• Because we divided by a negative number

• Because we divided by a positive number

• Because we subtracted a number from both sides

• Because we added a number to both sides

What is the final solution for the inequality -3x ≥ 21?

• x < 7

• x > -7

• x ≤ -7

• x ≥ 7

What is the result of dividing both sides of 4x ≤ -4 by 4?

• x < -1

• x ≥ -1

• x > -1

• x ≤ -1

If you have an inequality -5x > -10, what happens to the inequality sign after dividing both sides by -5?

• It changes to =

• It changes to <

• It changes to ≥

• It remains >

What is a key difference between solving equations and inequalities?

• Equations are solved without any arithmetic operations.

• Inequalities require you to use different numbers.

• Inequalities do not allow the use of negative numbers.

• Equations always use the equal sign, while inequalities can use >, <, ≥, ≤.