Graphing Linear Inequalities and Word Problems

Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new bike. Which inequality represents how long Johnny needs to work to afford his new bike?

• 15h ≤ 105

• 15h > 105

• 15h < 105

• 15h ≥ 105

Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks.
Which inequality could help you find how many dogs Katie would have to walk to reach her goal?

• 25 - 12x ≥ 200

• 25 + 12x ≥ 200

• 13x ≥ 200

• 25 + 12x < 200

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.

• 80+9.50x > 120+7.50x

• 80+9.50x < 120+7.50x

• 80x+9.50 > 120x+7.50

• 80x+9.50 < 120x+7.50

Cody’s Gym charges a $18 fee to join and $30 per month. Tyler’s Gym charges a $50 fee to join and $20 per month. Write an inequality that could be used to determine how many months you will have to go to the gym before Tyler’s gym would be the better deal.

• 50 + 20x < 18 + 30x

• 50x + 20 < 18x + 30

• 50 + 20x > 18 + 30x

• 50x + 20 > 18x + 30

The budget for a banquet is $1,900. If it costs $3.75 to serve a single meal at this banquet, which inequality describes the possible numbers of meals (m) that can be served?

Read each answer choice carefully!

Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks.
Use an inequality to find how many dogs Katie must walk in order to meet her goal.

• 14

• 15

• 18

• 19

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

• <

• >

• ≤

• ≥

A rectangle has a length that is seven inches longer than its width (w). If the perimeter of this rectangle is at most 30 inches, which of the following inequalities gives the possible values of "w"?