Solving Linear Inequalities and Graphing Solutions

This video tutorial focuses on solving inequalities and graphing them on a number line. It begins with an introduction to inequalities, followed by several examples demonstrating how to solve different types of inequalities, including simple and compound inequalities. Each example includes step-by-step instructions on solving the inequality and graphing the solution on a number line. The tutorial also covers the use of interval notation to represent solutions and highlights the importance of changing the inequality sign when multiplying or dividing by a negative number.

What is the first step in solving an inequality?

• Changing the direction of the inequality sign

• Graphing on a number line

• Dividing both sides by the coefficient of the variable

• Subtracting a constant from both sides

How do you represent a solution that is greater than a number but not equal to it on a number line?

• By shading towards the right

• With a closed circle

• With an open circle

• By shading towards the left

In the context of inequalities, what does shading towards the right on a number line indicate?

• The solution includes the number itself

• The solution is greater than a certain number

• The solution is less than a certain number

• The solution does not include the number itself

When solving an inequality involving a fraction, what is a crucial step?

• Changing the direction of the inequality sign

• Graphing the solution

• Multiplying both sides by the denominator

• Adding a constant to both sides

How is a solution that includes the number itself represented on a number line?

• With a closed circle

• With an open circle

• By shading towards positive infinity

• By shading towards negative infinity

What does a closed circle on a number line represent?

• The solution includes the number itself

• The solution is less than the number

• The solution is greater than the number

• The solution does not include the number itself

What is the interval notation for a solution that is less than or equal to a certain number?

• From the number to negative infinity

• From negative infinity to the number, using parentheses

• From negative infinity to the number, using brackets

• From the number to positive infinity

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

• Multiply both sides by the same negative number

• Add a constant to both sides

• Change the direction of the inequality sign

• Graph the solution on a number line

What special consideration is there when dividing both sides of an inequality by a negative number?

• You must add a constant to both sides

• You must subtract a constant from both sides

• There is no special consideration

• You must change the direction of the inequality sign

How do you solve a compound inequality?

• By treating each part of the inequality separately

• By multiplying both sides by a constant

• By adding a constant to one side only

• By graphing each inequality on separate number lines