Exploring Inequalities: Solving and Graphing Techniques

This video tutorial covers the concept of inequalities, explaining how they compare expressions using symbols like less than, greater than, and not equal to. It demonstrates how to graph inequalities on a number line and discusses the properties of inequalities, including addition, subtraction, multiplication, and division. The tutorial also shows how to solve inequalities using models and inverse operations, emphasizing the importance of isolating the variable. The video concludes by highlighting the continuity of learning and the importance of understanding each lesson.

What is an inequality?

• A mathematical sentence that compares two expressions using symbols like <, >, ≤, ≥, or ≠.

• A mathematical sentence that only uses multiplication and division.

• A mathematical sentence that only uses addition and subtraction.

• A mathematical sentence that uses an equal sign.

Which of the following is a solution to the inequality X > 3?

• 4

• 3

• 2

• 1

How is a number that is not a solution represented on a number line?

• With a filled-in circle.

• With an empty circle.

• With a triangle.

• With a square.

What does a filled-in circle on a number line indicate?

• The number is less than the solution.

• The number is not a solution.

• The number is a solution.

• The number is greater than the solution.

What do the addition and subtraction properties of inequalities state?

• You can add or subtract the same number on both sides of an inequality, and it will still be true.

• You cannot add or subtract any number on both sides of an inequality.

• You can only add the same number on both sides of an inequality.

• You can only subtract the same number on both sides of an inequality.

What happens when you subtract the same number from both sides of an inequality?

• The inequality becomes false.

• The inequality remains true.

• The inequality becomes an equation.

• The inequality becomes undefined.

What do the multiplication and division properties of inequalities state?

• You cannot multiply or divide any number on both sides of an inequality.

• You can only divide both sides of an inequality.

• You can multiply or divide both sides of an inequality by the same positive number, and it will still be true.

• You can only multiply both sides of an inequality.

If you divide both sides of the inequality 8 > 6 by 2, what is the resulting inequality?

• 8 > 3

• 4 > 3

• 4 < 3

• 8 < 3

What is the solution to the inequality X + 2 < 6?

• X ≤ 4

• X = 4

• X > 4

• X < 4

How is the inequality X - 3 ≥ 4 solved?

• By dividing both sides by 3.

• By multiplying both sides by 3.

• By subtracting 3 from both sides.

• By adding 3 to both sides.