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📝 No more than inequality meaning and examples (14 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 14 questions available

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What is No more than inequality meaning and examples?

Definition:
No more than" in inequality problems means the quantity is less than or equal to a certain value represented by the symbol $\le$ and it indicates a maximum allowable amount meaning the value cannot exceed the stated figure and this is used for limits like budget capacity or maximum time.

Working:
To translate "no more than use $\le$ and set the variable on the left side; for example, no more than 100" translates to $x \le 100$ and when solving the solution includes the boundary and all values less than it which is crucial for adhering to limits and graphs show a closed circle at the boundary with an arrow to the left.

Example:
A box can hold no more than 50 pounds; if each book weighs 2 pounds and the box already has 10 books then the inequality for additional books $x$ is $2(10 + x) \le 50$ so $20 + 2x \le 50$ $2x \le 30$ $x \le 15$ meaning at most 15 additional books can be added.

Reason:
Understanding "no more than" is vital for staying within limits such as weight capacity budget constraints and safety regulations and it helps in making decisions that respect maximum allowable values."

Easy

Medium

Hard

📝 All No more than inequality meaning and examples MCQs

Q1. A warehouse can hold no more than 240 boxes. Which inequality correctly represents the possible number $x$ of boxes stored?

x<240

x\le240

✅

x>240

x\ge240

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The phrase 'no more than' includes the maximum value itself, so 240 boxes are allowed. Therefore the number of boxes must be less than or equal to 240, represented by $x\le240$ .

Q2. A student interprets 'no more than 18 minutes' as meaning the time must be strictly less than 18 minutes. Which value shows why this interpretation is incorrect?

A.17 minutes

B.17.5 minutes

C.18 minutes ✅

D.18.5 minutes

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: 'No more than 18 minutes' means the time cannot exceed 18 minutes, so exactly 18 minutes is permitted. The strict inequality $t<18$ would incorrectly exclude a valid boundary value.

Q3. A theater has 500 seats, and 372 tickets have already been sold. If $x$ represents additional tickets that may be sold, which inequality models the situation?

372+x<500

372+x\le500

✅

372-x\le500

x-372\le500

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The total number sold after additional sales is $372+x$ . Since the theater can contain no more than 500 people, this total may equal 500 but cannot exceed it, giving $372+x\le500$ .

Q4. A delivery service charges a fixed fee of $12 plus$ 3 per package. A customer can spend no more than $45. What is the greatest whole number of packages the customer can send?

A.9

B.10 ✅

C.11

D.12

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The cost is $12+3x$ , and the spending limit gives $12+3x\le45$ . Subtracting 12 gives $3x\le33$ , so $x\le11$ . Thus the greatest whole number is 11, making option C correct.

Q5. A factory worker earns $18 per hour and wants to keep weekly earnings from this job at no more than$ 270. If $h$ is the number of hours worked, which solution set is correct?

h\ge15

h>15

h\le15

✅

h<15

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Weekly earnings are $18h$ . The condition 'no more than $270' requires $18h\le270$ . Dividing by 18 gives $h\le15$ . Therefore 15 hours is allowed while any amount above 15 hours violates the limit.

Q6. A student solves $5x-7\le18$ by adding 7 and then dividing by 5, obtaining $x\le5$ . Is the student's solution correct?

A.Yes, because all operations preserve the inequality.

B.No, the correct solution is

x\le25

C.No, the correct solution is

x\le5

. ✅

D.No, the correct solution is

x\ge5

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Adding 7 gives $5x\le25$ , and dividing by the positive number 5 gives $x\le5$ . The student's final result is therefore correct, illustrating that solving a 'no more than' condition can produce a closed upper boundary.

Q7. A graph represents the acceptable values for a quantity $x$ with a filled dot at 8 and shading extending to the left. Which inequality matches the graph?

x<8

x\le8

✅

x>8

x\ge8

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: A filled dot means the boundary value 8 is included. Shading to the left represents values smaller than 8. Combining both observations gives $x\le8$ , which correctly expresses 'no more than 8'.

Q8. A student claims that $4x+6\le30$ gives $x\le9$ . Another student claims it gives $x\le6$ . Which evaluation is correct?

A.The first student is correct.

B.The second student is correct. ✅

C.Both are incorrect; the solution is

x\le24

D.Both are correct because the inequality has two possible answers.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Subtracting 6 from both sides gives $4x\le24$ . Dividing by 4 gives $x\le6$ . The first student likely divided 30 by 4 without first accounting for the constant term, a common modeling error.

Q9. A graph shows the feasible values for $x$ as all points from $-3$ through 4, with both endpoints included. Which inequality represents this interval?

-3<x<4

-3\le x\le4

✅

x\le-3

x\ge4

-3\ge x\ge4

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Because both endpoints are included, the inequality signs must be inclusive. The graph contains every value between -3 and 4, so the correct compound inequality is $-3\le x\le4$ .

Q10. A school bus can carry no more than 48 students. There are already 31 students on the bus. If $x$ more students may board, which value of $x$ is the largest possible?

A.16

B.17 ✅

C.18

D.19

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The capacity condition is $31+x\le48$ . Subtracting 31 gives $x\le17$ . Therefore, 17 additional students can board, bringing the total exactly to 48. Eighteen would exceed the capacity.

Q11. A rectangular garden has length $x+4$ meters and width 6 meters. The owner wants its perimeter to be no more than 44 meters. What is the greatest possible value of $x$ ?

A.11

B.12

C.13 ✅

D.14

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The perimeter is $2(x+4)+2(6)=2x+20$ . The condition gives $2x+20\le44$ , so $2x\le24$ and $x\le12$ . Thus the greatest possible value is 12, making option B correct.

Q12. A budget allows no more than $100 for notebooks and pens. Notebooks cost$ 8 each and pens cost $2 each. If 7 notebooks are required, what is the greatest number of pens that can be purchased?

A.18

B.20

C.22 ✅

D.24

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Seven notebooks cost $7(8)=56$ dollars. The remaining budget is $100-56=44$ dollars. Since each pen costs $2, $2p\le44$ , giving $p\le22$ . Thus 22 pens is the greatest feasible number.

Q13. A machine must process no more than 120 units in a shift. It has already processed 35 units and processes 55 units every minute. What is the greatest number of complete minutes it can continue operating without exceeding the limit?

A.16

B.17 ✅

C.18

D.19

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The total after $m$ additional minutes is $35+5m$ . The capacity condition is $35+5m\le120$ . Thus $5m\le85$ , giving $m\le17$ . Therefore, the machine can operate for at most 17 additional complete minutes.

Q14. For real $x$ , suppose $x$ is an integer and $3(2x-1)\le27$ . A student divides by 3, obtains $2x-1\le9$ , then concludes $x\le4$ . What is the correct conclusion?

A.The student is correct:

x\le4

. ✅

B.The correct conclusion is

x\le5

C.The correct conclusion is

x\ge5

D.There is no solution because

x

must be positive.

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Dividing by positive 3 gives $2x-1\le9$ . Adding 1 produces $2x\le10$ , and dividing by 2 gives $x\le5$ . Therefore, the student's conclusion $x\le4$ is incorrect; 5 satisfies the original inequality exactly.

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