Inequalities in One Variable

What is the solution to the inequality 5.25 - b ≥ 6.5?

A

Xavier can work no more than 40 hours in a week. He has already worked 24 hours this week. What is the maximum number of 8-hour days can he work for the rest of the week?

A. 2

What is the best first step to solve the inequality 5x - 3 ≥ 2?

A. Add 3 to both sides of the equation.

What is the first step in solving the inequality < -1?

A. Multiply both sides by 6.

A phone plan has a limit of $25 that can be spent on text messages. The base cost of the text plan will cost a user $5. Each text will cost $0.05. How many text messages (t) can a user send without exceeding the plan limits?

A. t ≤ 400

What is the solution to the inequality + 4 ≤ 0?

B. (-∞, -28]

Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30?

B. 30n + 60 < 150

Mrs. Valdez wanted to determine the number of people, p, she could safely take in her car to the fun run. She determined that p < 5. Which statement best describes a possible number of people she can take in her car?

B. Mrs. Valdez can take 2 people because 2 < 5.

What is the first step in solving the inequality 2x + 3 ≥ 17?

B. Subtract 3 from both sides.

Solve. 2a + 4 > 12

B. {a | a > 4}

The solution to an inequality is graphed on the number line. What is another way to represent this solution set?

B. {x | x ≤ 4.5}

Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate's problem?

C. The shelter can house 17 cats because 17 < 28.

The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Check all that apply.

NOT A B D (C & E are correct)