Graphing and Solving Inequalities

The video tutorial guides viewers through solving and graphing a linear inequality. It begins with simplifying the inequality using the distributive property, followed by solving for x through subtraction and division. The solution is then graphed on a number line, with an explanation of how to test values to verify the solution. The tutorial concludes with a summary of the process.

What is the first step in solving a linear inequality?

• Graphing the inequality

• Simplifying the inequality

• Testing values

• Checking the solution

Which property is used to simplify the inequality 4x + 12 ≤ 44?

• Identity Property

• Commutative Property

• Distributive Property

• Associative Property

After applying the distributive property, what is the next step in solving the inequality 4x + 12 ≤ 44?

• Multiply both sides by 4

• Subtract 12 from both sides

• Add 12 to both sides

• Divide both sides by 4

What is the solution to the inequality 4x + 12 ≤ 44 after simplification?

• x > 8

• x < 8

• x ≥ 8

• x ≤ 8

Where should you start the number line when graphing the solution x ≤ 8?

• At 10

• At 5

• At 8

• At 0

What does shading the circle at 8 on the number line indicate?

• 8 is part of the solution

• 8 is not part of the solution

• The solution starts at 9

• The solution ends at 7

Which of the following values is part of the solution for x ≤ 8?

• 11

• 10

• 9

• 8

What is the result of testing the value 10 in the inequality x ≤ 8?

• Partially true

• False

• Undefined

• True

Why is it important to test values when graphing inequalities?

• To confirm the solution is correct

• To make the graph look better

• To find the exact solution

• To check for errors in calculation

What does the inequality x ≤ 8 represent on a number line?

• All numbers less than or equal to 8

• All numbers greater than 8

• Only the number 8

• All numbers less than 8