Inequalities and Their Solutions

The video tutorial explains how to find solutions to an inequality by simplifying and solving it. It begins by defining what a solution to an inequality is and then demonstrates how to simplify the inequality using properties of equality. The tutorial continues by solving the inequality, highlighting the importance of flipping the inequality sign when dividing by a negative number. Finally, it verifies which numbers satisfy the inequality, using examples to illustrate the process.

What is a solution to an inequality?

• A number that makes the inequality false

• A number that makes the inequality true

• A number that makes the equation true

• Any random number

What is the first step in simplifying the inequality -5x - 9 ≤ 11 + 5x?

• Multiply both sides by 10

• Subtract 5x from both sides

• Divide both sides by -5

• Add 9 to both sides

After simplifying, what is the inequality before dividing by -10?

• 10x ≥ 20

• 10x ≤ 20

• -10x ≥ 20

• -10x ≤ 20

What must you remember to do when dividing both sides of an inequality by a negative number?

• Subtract 10 from both sides

• Add 10 to both sides

• Keep the inequality sign the same

• Flip the inequality sign

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

• It disappears

• It stays the same

• It flips direction

• It becomes an equal sign

Which of the following numbers is NOT a solution to the inequality x ≥ -2?

• 20

• 2

• -2

• -20

Why is -20 not a solution to the inequality x ≥ -2?

• Because -20 is not a number

• Because -20 is greater than -2

• Because -20 is less than -2

• Because -20 is equal to -2

Which of the following is a correct solution to the inequality x ≥ -2?

• -4

• -3

• -5

• -1

Which of the following is a solution to the inequality x ≥ -2?

• -10

• 0

• -3

• -5