Framing/writing linear inequalities in one variable

A new van is priced at $19,500. If the buyer chooses to finance, he or she will pay $5,000 as a down payment and $375 per month. Which inequality can be used to find out after how many months will the buyer have paid more than $10,000 towards the van?

•  $19,500\ -5000x\ \ >10,000$  

•  $5000x\ +\ 375\ >\ 10,000$  

•  $5000\ +\ 375x\ >\ 10,000$  

•  $19,500\ -375x\ <10,000$  

Olivia gets 5 points for each answer and has already earned 10 points of extra credit She needs at least 77 points to pass.

• 10a + 5 ≥ 77

• 5a + 10 ≥ 77

• 5a + 10 > 77

• 5a + 10 ≤ 77

The 30 members of a choir are trying to raise at least $1,500 to cover travel costs to a singing camp. They have already raised $600. Which inequality could you solve to find the average amounts each member can raise that will at least meet the goal?

• 30x + 600 > 1,500

• 30x + 600 ≥ 1,500

• 30x + 600 < 1,500

• 30x + 600 < 1,500

The speed limit is 45. Katie was going thirty miles per hour and sped up some. Which inequality represents the amount she could speed up and not be speeding? 

• 30 + s ≥ 45
• 30 - s ≥ 45
• 30 + s ≤ 45
• 30 - s ≤ 45

Write an inequality for the following: 5 less than twice some number is more than 15

• 5 - 2x > 15

• 5 - 2x < 15

• 2x - 5 < 15

• 2x - 5 > 15

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?

• 1.75m + 0.65 ≥ 10

• 1.75m + 0.65 > 10

• 1.75 + 0.65m ≤ 10

• 1.75 + 0.65m < 10

Four times a number increased by  7 is at least 19. 

• 4x > 19
• 4x + 7 ≥ 19
• 4x < 19
• 4x + 7 ≤ 19

Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff did not spend more than $14 on the hot dogs and the bottle of water. Which inequality can be used to find h, the number of hot dogs that Jeff could have bought?

• $3h\ -\ 2\ \le14$

• $3h\ -2\ \ge14$

• $3h\ +2\ \le14$

• $3h\ +\ 2\ \ge14$

Sheila had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• 500 - 25x ≥ 200

• 500 - 25x ≤ 200

• 500 + 25x ≥ 200

• 200 + 25x ≥ 500

Stacy has $25 in her savings account. To save more money, Stacy is selling lemonade for $0.50. She wants to have more than $150 in her account. Which inequality represents this situation?