Solving Multi-Step Inequalities in Word Problems

This video tutorial covers how to write and solve inequalities from word problems. It begins with an introduction to the process, including writing a let statement, forming the inequality, solving it, and writing a conclusion. Two examples are provided: one involving Dan's vacuum sales and another about Ariana's cheese purchase. The video emphasizes understanding keywords like 'at least' and 'no more than' to choose the correct inequality symbol. It also highlights the importance of rounding appropriately when dealing with real-world quantities.

What is the first step in writing inequalities from word problems?

• Solve the inequality

• Write a let statement

• Write a conclusion

• Refer to notes

What does the keyword 'at least' indicate in an inequality?

• Greater than or equal to

• Less than or equal to

• Greater than

• Less than

Dan earns $100 per day plus $12 per vacuum sold. How many vacuums must he sell to earn at least $250?

• 15

• 10

• 12

• 13

Why do we round up the number of vacuums Dan must sell to 13?

• To account for taxes

• To make the calculation easier

• To ensure he earns at least $250

• Because 12.5 is not a whole number

Ariana can spend no more than $40. What does 'no more than' mean in terms of inequality?

• Greater than or equal to

• Less than

• Less than or equal to

• Greater than

Ariana already bought 4 boxes of crackers for $3.50 each. How much did she spend on crackers?

• $14

• $16

• $12

• $10

If Ariana wants to buy 4 blocks of cheese, what is the maximum cost per block of cheese she can afford?

• $7.00

• $6.50

• $5.50

• $6.00

What is the inequality used to determine the maximum cost per block of cheese Ariana can buy?

• 4(3.50 + c) < 40

• 4(3.50 + c) > 40

• 4(3.50 + c) ≤ 40

• 4(3.50 + c) ≥ 40

What is the final step in solving an inequality from a word problem?

• Write a let statement

• Solve the inequality

• Write a conclusion

• Refer to notes

What should you do if the solution to an inequality involves a non-whole number in a context where only whole numbers make sense?

• Ignore the context

• Leave it as is

• Round down

• Round up