Inequalities and Real-World Applications

The video tutorial covers solving multi-step inequalities in various word problems. It begins with an introduction to the concept, followed by practical examples involving cost comparisons between businesses, music service pricing, and temperature changes in Texas cities. The tutorial concludes with real-world scenarios that can be represented by inequalities, emphasizing problem-solving skills.

What is the first step in solving a multi-step inequality?

• Add all constants to one side

• Multiply both sides by zero

• Divide by the largest coefficient

• Isolate the variable on one side

Ocean Adventures charges $35 per hour plus $14 for a wetsuit. What is the expression for the total cost for h hours?

• 35 + 14h

• 35h + 14

• 14h + 35

• 35h - 14

Water Fan Inc. charges $22 per hour plus $40 for a wetsuit. What inequality represents when Ocean Adventures is cheaper?

• 35h + 14 < 22h + 40

• 35h + 14 = 22h + 40

• 35h + 14 ≥ 22h + 40

• 35h + 14 > 22h + 40

After solving the inequality for Ocean Adventures and Water Fan Inc., what is the maximum number of hours for which Ocean Adventures is cheaper?

• 4 hours

• 3 hours

• 2 hours

• 1 hour

Music Incorporated charges a membership fee of $9.99 plus $0.99 per song. What is the expression for the total cost for x songs?

• 9.99x + 0.99

• 0.99x + 9.99

• 9.99 + 0.99x

• 0.99 + 9.99x

Your Choice Music charges $1.99 per song with no membership fee. What inequality represents when Your Choice Music is cheaper or equal?

• 1.99x ≤ 9.99 + 0.99x

• 1.99x > 9.99 + 0.99x

• 1.99x < 9.99 + 0.99x

• 1.99x ≥ 9.99 + 0.99x

What is the maximum number of songs for which Your Choice Music is cheaper or equal to Music Incorporated?

• 9 songs

• 11 songs

• 10 songs

• 9.99 songs

In Brownsville, the temperature is 88°F and drops 1.5°F per hour. What is the expression for the temperature after h hours?

• 88h - 1.5

• 88 + 1.5h

• 88 - 1.5h

• 1.5h - 88

In Mesquite, the temperature is 94°F and drops 2°F per hour. What inequality represents when Mesquite is warmer than Brownsville?

• 94 - 2h < 88 - 1.5h

• 94 - 2h ≥ 88 - 1.5h

• 94 - 2h > 88 - 1.5h

• 94 - 2h = 88 - 1.5h

Which real-world scenario can be represented by the inequality 100 + 6n < 8.5n?

• Car rental cost

• Melanie's gym membership

• Franca's baseball cards

• Maria's phone plan