Properties and Solutions of Inequalities

The video tutorial covers solving linear equations and inequalities with one variable. It begins with an introduction to the topic, followed by a review of solution sets and graphing inequalities. The addition property of inequalities is explained, showing how adding or subtracting the same number from both sides of an inequality does not change its solution set. The positive multiplication property is also discussed, demonstrating that multiplying both sides by a positive number maintains the inequality's direction. The tutorial concludes with examples of solving inequalities using these properties.

What is the main focus of the lesson introduced by Kandace and Ann?

• Graphing polynomial functions

• Understanding complex numbers

• Solving linear equations with one variable

• Solving quadratic equations

How is the solution set for the inequality Y < 7 represented on a number line?

• With a closed circle at 7 and shading to the right

• With an open circle at 7 and shading to the right

• With a closed circle at 7 and shading to the left

• With an open circle at 7 and shading to the left

What does the addition property of inequalities state?

• Adding the same number to both sides of an inequality changes the solution set

• Adding the same number to both sides of an inequality does not change the solution set

• Subtracting the same number from both sides of an inequality changes the solution set

• Multiplying both sides of an inequality by a negative number does not change the solution set

Which of the following inequalities is equivalent to X > 2?

• X < 2

• 2 < X

• X = 2

• X ≤ 2

What happens when you add the same number to both sides of an inequality?

• The inequality becomes invalid

• The inequality becomes an equation

• The inequality sign remains the same

• The inequality sign flips

How do you verify the solution to an inequality after using the addition property?

• By checking only the endpoint

• By checking both the endpoint and an interior point

• By graphing the inequality

• By checking only an interior point

What is the positive multiplication property of inequalities?

• Multiplying both sides by zero changes the inequality to an equation

• Multiplying both sides by a negative number does not change the inequality sign

• Multiplying both sides by a positive number does not change the inequality sign

• Multiplying both sides by a positive number changes the inequality sign

What is the result of multiplying a negative number by a positive number in an inequality?

• The inequality becomes an equation

• The result is a positive number

• The inequality sign flips

• The result is a negative number

How do you solve the inequality 2W ≥ -10?

• Divide both sides by 2

• Subtract 10 from both sides

• Multiply both sides by 2

• Add 10 to both sides

What happens when you divide both sides of an inequality by a positive number?

• The inequality sign flips

• The inequality becomes an equation

• The inequality sign remains the same

• The inequality becomes invalid