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📝 Exceeds inequality meaning and examples (12 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 12 questions available

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What is Exceeds inequality meaning and examples?

Definition:
Exceeds" in inequality problems means the quantity is greater than a certain value represented by the symbol $>$ and it indicates that the value is strictly above the stated amount not including the boundary meaning it must be more than the given number and this is used for thresholds like exceeding a speed limit or surpassing a target.

Working:
To translate "exceeds use $>$ and set the variable on the left side; for example, exceeds 100" translates to $x > 100$ and when solving the solution does not include the boundary (open circle on graph) and all values greater than the boundary are acceptable and this is crucial for surpassing minimum targets or alerting limits.

Example:
If a car's speed exceeds 60 mph it triggers a warning; if the speed is $s$ then $s > 60$ meaning any speed greater than 60 mph violates the limit and if a company's profit exceeds $\$10000$ then $P > 10000$ indicating a successful outcome.

Reason:
"Exceeds" is important in contexts like safety thresholds performance targets and quality standards where exceeding a value indicates a condition that must be monitored or achieved and it helps in setting goals and alerts."

Easy

Medium

Hard

📝 All Exceeds inequality meaning and examples MCQs

Q1. Which inequality correctly represents the statement: a number $x$ exceeds 12?

x<12

x\le12

x>12

✅

x\ge12

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The phrase 'exceeds 12' means the number is strictly greater than 12. Therefore equality is not included, so the correct mathematical representation is $x>12$ .

Q2. A school requires a student to score a mark that exceeds 70 to qualify. Which score satisfies the requirement?

A.70

B.69

C.70.5 ✅

D.Any score below 70

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Because the score must exceed 70, it must be strictly greater than 70. A score of exactly 70 does not qualify, while 70.5 is greater than 70 and therefore satisfies the inequality.

Q3. A taxi charges a fixed fee of 250 rupees plus 40 rupees per kilometer. If the total fare exceeds 650 rupees, which inequality describes the distance $d$ ?

250+40d<650

250+40d>650

✅

40d-250>650

250d+40>650

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The total fare is modeled by $250+40d$ . Since the fare exceeds 650 rupees, the model must satisfy $250+40d>650$ . The wording requires a strict greater-than relationship.

Q4. A student solves $3x+5>20$ and writes $x>5$ . What is the best evaluation of the student's reasoning?

A.Correct, because 5 is the boundary value

B.Incorrect; the correct solution is

x>5

only if 5 is excluded ✅

C.Incorrect; the correct solution is

x>25

D.Correct, because adding 5 increases the inequality

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Subtracting 5 from both sides gives $3x>15$ , and dividing by 3 gives $x>5$ . Thus the student's final answer is actually correct, although the reasoning should explicitly show both algebraic steps.

Q5. A delivery company allows a package weight to exceed 20 kg but charges an additional fee when it does. Which statement describes the charged packages?

w<20

w\le20

w=20

w>20

✅

💡 Difficulty: medium | ✅ Correct: D

📖 Explanation: The word 'exceed' indicates a value strictly greater than the stated amount. Therefore packages with weights greater than 20 kg, represented by $w>20$ , incur the additional fee.

Q6. A graph shows a horizontal boundary at $y=8$ , and the shaded region lies above the boundary without including the boundary line. Which inequality represents the shaded region?

y<8

y\le8

y>8

✅

y\ge8

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: A region above $y=8$ represents values greater than 8. Because the boundary itself is not included, the inequality must be strict, giving $y>8$ .

Q7. A learner claims that $2x-6>10$ has solution $x>2$ . Which response correctly identifies the error?

A.The learner should add 6 instead of subtracting it

B.The learner forgot to divide by 2 after adding 6 ✅

C.The inequality sign should become less than

D.The constant 10 should be divided first

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Adding 6 to both sides gives $2x>16$ . Dividing by 2 then gives $x>8$ . The learner stopped too early after obtaining $2x>16$ , so $x>2$ is not the correct solution.

Q8. A runner's speed $v$ must exceed 9 m/s. Another runner must have a speed of at least 9 m/s. Which comparison is correct?

A.Both require

v>9

B.Both require

v\ge9

C.The first requires

v>9

, while the second allows

v=9

✅

D.The first allows

v=9

, while the second requires

v>9

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: 'Exceeds 9' means strictly greater than 9, so $v>9$ . 'At least 9' means 9 or greater, so $v\ge9$ . The distinction is whether the boundary value is included.

Q9. A company's revenue graph has a dashed horizontal line at $y=50$ , with the region above it shaded. What conclusion can be drawn?

A.Revenue is less than or equal to 50

B.Revenue exceeds 50 ✅

C.Revenue is exactly 50

D.Revenue is less than 50

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: A dashed boundary indicates that the boundary value is excluded. Since the shaded region is above $y=50$ , the represented values satisfy $y>50$ , meaning the revenue exceeds 50.

Q10. A machine operates only when its temperature $T$ exceeds 75°C. A technician records 74°C, 75°C, 75.1°C, and 80°C. Which readings indicate that the machine can operate?

A.74°C and 75°C

B.75°C and 75.1°C

C.75.1°C and 80°C ✅

D.All four readings

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The condition is $T>75$ , so exactly 75°C is not sufficient. The readings 75.1°C and 80°C are both strictly greater than 75°C and therefore satisfy the operating condition.

Q11. A budget is described by $B=500+25x$ , where $x$ represents optional items purchased. The budget must exceed 800. A student says $x>12$ , while another says $x>12.5$ . Who is correct?

A.Only the first student

B.Only the second student ✅

C.Both students

D.Neither student

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The condition is $500+25x>800$ . Subtracting 500 gives $25x>300$ , so $x>12$ . If $x$ must be a whole number, the smallest possible value is 13. Thus the algebraic condition is $x>12$ , making the first student correct.

Q12. For positive $x$ , a model requires both $x>6$ and $2x+1>15$ . What is the combined solution?

x>6

x>7

✅

x>8

x>15

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The first condition gives $x>6$ . The second gives $2x>14$ , hence $x>7$ . Both conditions must hold simultaneously, so their intersection is $x>7$ . The stricter condition determines the final solution.

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