Understanding Inequalities

The video tutorial explains how to represent scenarios using inequalities, focusing on graphing values on a number line and forming compound inequalities. It uses examples like height and biking distance to illustrate the concepts, emphasizing the importance of open and closed points to indicate whether endpoints are included in the solution. The tutorial also discusses how to determine if an inequality is true or false for specific values, providing practical examples to reinforce understanding.

What does it mean when an inequality is described as 'strictly between' two values?

• The values are less than the endpoints.

• The values are equal to the endpoints.

• The values exclude the endpoints.

• The values include the endpoints.

How do you represent an open point on a number line?

• By marking the point with an 'X'.

• By leaving the point unshaded.

• By shading the point.

• By drawing a circle around the point.

Which inequality symbol represents 'greater than'?

• ≤

• >

• <

• =

If h is strictly between 60 and 66, which of the following values of h makes the inequality false?

• 65

• 61

• 63

• 60

Which of the following values of h makes the inequality h > 60 and h < 66 true?

• 62

• 66

• 60

• 70

What is the compound inequality for a value m that is at least 32 but less than 52?

• m > 32 and m < 52

• m ≥ 32 and m < 52

• m > 32 and m ≤ 52

• m ≥ 32 and m ≤ 52

In the context of inequalities, what does a closed point on a number line indicate?

• The value is part of the solution.

• The value is not part of the solution.

• The value is less than the solution.

• The value is greater than the solution.

Which value of m makes the inequality m ≥ 32 and m < 52 false?

• 32

• 50

• 31

• 33

If m is greater than or equal to 32 and less than 52, which of the following is a valid value for m?

• 53

• 31

• 32

• 52

What does it mean if an inequality is false for a boundary value?

• The boundary value is included in the solution.

• The boundary value is not included in the solution.

• The boundary value is equal to the solution.

• The boundary value is greater than the solution.