Inequality Word Problems with Variables on Both Sides

Which inequality is represented by the words "less than"?

• <
• >
• ≤
• ≥

Which inequality is represented by the words " at least"?

• <
• >
• ≤
• ≥

Which inequality is represented by the words " more than"?

• <
• >
• ≤
• ≥

Which inequality is represented by the words " no more than" or "at most"?

• <
• >
• ≤
• ≥

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10
• 1.75 + 0.65m > 10
• 1.75m + 0.65 < 10
• 1.75m + 0.65 > 10

Twice a certain number, increased by 5, is less than three times the same number.

• 2x + 5 > 3x
• 2x + 5 < 3x
• 2x + 5 ≤ 3x
• 2x + 5 ≥ 3x

Renting games online from Netwii costs $3.33 per game  with no monthly fee.  Renting games online from HDO costs $2.00 per game plus a monthly fee of $10.00.
Which inequality represents the situation when the monthly cost at Netwii is more than the monthly cost at HDO?

• 3.33v > 2v + 10
• 3.33v + 10 > 2v 
• 3.33v < 2v + 10
• 3.33v + 10 < 2v

The inequality shown below represents fees for two different apartments.

500x + 700 < 650x + 200

Which situation below does this inequality represent?

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is equal to Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is greater than Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 per month and then $500 deposit. Apartment B is greater than Apartment A charging $650 deposit with $200 per month.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is less than Apartment A charging $650 per month with a $200 deposit.

Printing A prints pictures for $0.10 each and a $50 membership fee.  Printing Q prints pictures for $2 each with no membership fee.  Which inequality would be used to determine when Printing A is greater than Printing Q?

• 0.1p + 50 > 2p
• 0.1p + 50 < 2p
• 50p + 0.1 < 2p
• 50p + 0.1 > 2p

Papaya charges $5 per DVD rental and a $10 membership fee.  Hutto charges $2 per DVD and a $60 membership fee.  Which inequality best represents when the charges from Papaya is less than Hutto?

• 10 + 5d < 60 + 2d
• 10 + 5d > 60 + 2d
• 10d + 5 < 60d + 2
• 12d > 70