Inequalities and Proportional Relationships

The video covers solving inequalities, analyzing concert ticket pricing, determining true inequalities with specific x values, drawing solution sets, and calculating percentage increases in height. It uses practical examples to explain mathematical concepts and problem-solving techniques.

In the inequality problem, what is the correct direction to shade if x is smaller than -10?

• Do not shade at all

• Shade to the right of -10

• Shade to the left of -10

• Shade both sides of -10

What is the minimum ticket price needed to ensure at least 600 people attend the concert?

• $6 or less

• $10 or more

• $8 or more

• $8 or less

If the ticket price is increased, what is likely to happen to the concert attendance?

• Attendance will double

• Attendance will remain the same

• Attendance will decrease

• Attendance will increase

Which inequality is true when x is substituted with -3?

• Opposite of x minus 6 is greater than -3.5

• Opposite of x minus 6 is equal to -3.5

• Opposite of x minus 6 is greater than 3.5

• Opposite of x minus 6 is less than -3.5

What is the solution set for the inequality x ≤ 5?

• All numbers greater than or equal to 5

• All numbers less than or equal to 5

• All numbers less than 5

• All numbers greater than 5

How do you represent the inequality x < 2.5 on a number line?

• Shade to the right of 2.5 with an open circle

• Shade to the left of 2.5 with an open circle

• Shade to the left of 2.5 with a filled circle

• Shade to the right of 2.5 with a filled circle

What was Claire's height in inches one year ago?

• 54 inches

• 48 inches

• 52 inches

• 58 inches

By what percentage did Claire's height increase over the year?

• 7.4%

• 8.4%

• 5.4%

• 6.4%

What is the constant of proportionality used to calculate Claire's height increase?

• 0.48

• 0.60

• 0.54

• 0.58

What is the new height of Claire in inches after her growth?

• 54 inches

• 56 inches

• 60 inches

• 58 inches