Graphing Inequalities and Number Lines

The video tutorial demonstrates how to solve an inequality by isolating the variable x. The process involves distributing numbers, simplifying expressions, and graphing the solution on a number line. The instructor explains each step clearly, ensuring that viewers understand how to test points and verify the solution.

What is the primary goal when solving an inequality?

• To find the value of y

• To isolate the variable x

• To eliminate all numbers

• To graph the solution

Why do we distribute the 2 in the inequality?

• To simplify the solution

• To add more terms

• To eliminate the parentheses

• To change the inequality sign

What is the result of distributing the 2 in the expression 2(x - 4)?

• 4x - 8

• 2x - 8

• 2x + 8

• 2x - 4

What is the next step after distributing the 2 in the inequality?

• Multiply both sides by 2

• Move all x terms to one side

• Add 4 to both sides

• Divide both sides by 2

How do you move all x terms to one side of the inequality?

• Add x to both sides

• Divide x on both sides

• Subtract x from both sides

• Multiply x on both sides

What operation is used to solve for x after moving terms?

• Subtraction

• Multiplication

• Addition

• Inverse operations

What is the inequality after solving for x?

• x is not equal to -7

• x is equal to -7

• x is less than -7

• x is greater than -7

What does an open dot on a number line indicate?

• The number is not included in the solution

• The number is a midpoint

• The number is included in the solution

• The number is the only solution

Why is the dot at -7 open in the graph?

• Because -7 is part of the solution

• Because -7 is a midpoint

• Because -7 is not part of the solution

• Because -7 is the only solution

What should you do after placing the open dot on the number line?

• Shade to the right of the dot

• Shade to the left of the dot

• Do not shade at all

• Shade the entire line