Exploring Inequalities: Solving and Graphing Techniques

The video tutorial covers solving and graphing inequalities, starting with basic concepts and moving to more complex examples involving variables. It explains how to graph solutions on a number line, check solutions, and handle special cases like dividing by negative numbers. The tutorial emphasizes understanding the direction of inequalities and the importance of checking solutions to ensure accuracy.

What does it mean when an inequality has a boundary point shaded in?

• The boundary point is not part of the solution.

• The inequality is invalid.

• The boundary point must be zero.

• The boundary point is part of the solution.

What does an open circle on a graphed inequality indicate?

• The inequality is an equation.

• The boundary point is part of the solution.

• The boundary point is not part of the solution.

• The graph is incomplete.

What is the purpose of shading in a direction on a graphed inequality?

• To indicate the range of valid solutions.

• To differentiate it from equations.

• To mark the inequality as solved.

• To highlight the boundary point.

When graphing 'X is less than or equal to 6', how is the boundary point represented?

• By leaving the boundary point unmarked.

• With an open circle at 6.

• With a shaded circle at 6.

• By shading towards the positive direction.

How do you solve an inequality with an additional term next to the variable?

• By subtracting the term from both sides.

• By dividing both sides by the term.

• By adding the inverse of the term to both sides.

• By multiplying both sides by the term.

How do you graph an inequality that includes a variable minus a number is greater than another number?

• By adding the number to both sides before graphing.

• By subtracting the number from both sides before graphing.

• By dividing both sides by the number.

• By multiplying both sides by the number.

In the context of inequalities, what does it mean to 'isolate the variable'?

• To multiply the variable by itself.

• To solve the inequality for zero.

• To remove the variable from the inequality.

• To get the variable by itself on one side of the inequality.

Why is it important to check the solution of an inequality?

• To verify the solution makes the inequality a true statement.

• To convert the inequality into an equation.

• To confirm the solution set includes zero.

• To ensure the inequality remains balanced.

What special consideration must be taken when dividing both sides of an inequality by a negative number?

• The inequality symbol remains the same.

• The solution becomes invalid.

• The inequality symbol must be reversed.

• Both sides of the inequality must be squared.

What happens to the inequality symbol when dividing both sides by a negative number?

• It remains unchanged.

• It is reversed.

• It changes to an equal sign.

• It is removed from the inequality.