Framing/writing linear inequalities in one variable

Write the word sentence as an inequality.

The difference of a number p and 2 is at least 5

• 
  

  $2-p\ge5$

• $p-2\ge5$

• $2-p\le5$

• $p-2\le5$

Gabriela is the manager of a print shop. She needs to schedule employees to work no more than 300 person-hours per week. She has one 20 hour a week part-time employee. Each full-time employee works 40 hours per week. Which inequality will determine f, the number of full-time employees Gabriela can schedule to remain under the 300 person-hour per week limit?

• $20\ +\ 40f\ \le\ 300$

• $40\ +\ 20f\ \ge\ 300$

• $20\ +\ 40f\ \ge\ 300$

• $20f\ +\ 40\ <\ 300$

You are getting paid to do chores around the house. Your mom already gave you $5 and will give you at $3 for each chore you complete. Which inequality shows how many chores you will have to do to earn at least $26?

• $3x+5<26$

• $3x+5>26$

• $3x+5\le26$

• $3x+5\ge26$

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

Your cell phone plan allows you 400 minutes to talk per month. So far this month, you have used 265 minutes and you have 7 days left on this month’s plan. Which inequality could you use to determine how many minutes at most you can use per day so that you don’t go over your monthly plan minutes?

• 7x + 265 < 400

• 7x + 265 ≤ 400

• 7x + 265 > 400

• 7x + 265 ≥ 400

Ella has a $30 online gift card. She plans to buy as many books as she can without spending more than her online card amount. The cost of each book is $4. There is also a single shipping charge of $2. Which inequality represents the situation described?

• None of the Above

• 8n + 30 ≤ 2

• 4n + 2 ≤ 30

• 16n + 8 ≤ 14

• 30 ≤ 2n + 4

You take a trip to the bowling alley, where each game costs ₹ 20, plus you plan to spend rs100 on food. You can spend at most ₹ 250. Which inequality models this scenario? ( x is number of games)

• 2x + 10 ≥ 25

• 2x + 10 > 20

• 2x + 10 ≤ 25

• 2x + 10 < 25

Nick had $26.50 to spend at the fair. Admission to the fair was $8.50 and rides cost $1.50 per ticket. Which inequality and solution represents how many ride tickets Nick can purchase?

• 8.50 + 1.50x < 26.50; Nick can purchase more than 12 tickets

• 8.50 + 1.50x > 26.50; Nick can purchase more than 12 tickets

• 8.50 + 1.50x ≤ 26.50; Nick can purchase no more than 12 tickets

• 8.50 + 1.50x ≥ 26.50; Nick can purchase no more than 12 tickets

Which inequality represents the following problem:
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 represents all of the possible number of square yards you could buy so that The Rug Store costs 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

Remington needs at least $3,000 to buy a used car. He already has $1,800. If he saves $50 per week, select an inequality to represent how many weeks he must save to buy the car.

• $1,800\ +\ 50w\ \ge\ 3,000$

• $1,800\ +\ 50w\ \le\ 3,000$

• $1,800\ +\ 50w\ >\ 3,000$