Online Test — Linear Inequalities
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
easy
A plumber charges ₹500 as a visiting fee plus ₹150 per hour. If a customer has a budget of strictly less than ₹1400, what is the maximum number of full hours the plumber can work?
4
5
6
7
Explanation: 500 + 150h < 1400 → 150h < 900 → h < 6. The maximum full hours (integer) is 5.
Question 2 of 10
medium
A taxi charges ₹50 as base fare and ₹12 per km. If you have ₹200, what is the maximum distance in km you can travel?
12
12.5
13
13.5
Explanation: 50 + 12d ≤ 200 → 12d ≤ 150 → d ≤ 12.5. The max distance is exactly 12.5 km.
Question 3 of 10
medium
Which statement is true if x ∈ (−1, 2]?
x can be 2
x can be −1
x must be greater than 2
x must be less than −1
Explanation: 2 is included while −1 is excluded.
Question 4 of 10
easy
Find the range of x for which both 3x + 2 > 8 and 2x − 5 < 7 hold true.
(2, 6)
[2, 6)
(2, 6]
No solution
Explanation: 3x > 6 → x > 2. 2x < 12 → x < 6. Overlap is 2 < x < 6.
Question 5 of 10
medium
A student needs at least 90 average marks in 5 exams to get an A grade. Her first 4 exams marks are 87, 92, 94, and 95. What is the minimum she needs in the 5th exam?
80
81
82
83
Explanation: (87 + 92 + 94 + 95 + x)/5 ≥ 90 → 368 + x ≥ 450 → x ≥ 82.
Question 6 of 10
medium
Which interval represents x > −5?
(−5, ∞)
[−5, ∞)
(−∞, −5)
(−∞, −5]
Explanation: −5 is excluded.
Question 7 of 10
medium
Find the smallest integer x which satisfies the inequality (x + 3)/2 − (x − 2)/3 > 1.
−5
−6
−7
−8
Explanation: Multiply by 6: 3x + 9 − 2x + 4 > 6 → x + 13 > 6 → x > −7. The smallest integer greater than −7 is −6.
Question 8 of 10
medium
Solve the inequality −15 < 3(x − 2)/5 ≤ 0.
(−23, 2]
[−23, 2)
(−23, 2)
[−23, 2]
Explanation: Multiply by 5: −75 < 3(x − 2) ≤ 0. Divide by 3: −25 < x − 2 ≤ 0. Add 2: −23 < x ≤ 2, i.e. the interval (−23, 2].
Question 9 of 10
easy
The graphical representation of x > 2 on a number line uses:
Open circle at 2
Closed circle at 2
Open circle at 0
Closed circle at 0
Explanation: 2 is not included in the solution.
Question 10 of 10
medium
Solve: 1/2 x + 3 > 7
x > 8
x < 8
x ≥ 8
x ≤ 8
Explanation: ½x > 4, therefore x > 8.