CBSE Class 11 Mathematics Linear Inequalities Worksheet

Q1. Solve 4x-7 ≥ 5x-2 when (i) x is a natural number (ii) x is an integer (iii) x is a real number.

Q2. Solve the following linear inequations, show the solution on number line:-
(i) 2x-3/4 + 9 ≥ 4x/3 
(ii) 3(x-2)/5 ≥ 5(2 – x)/3 
(iii) x + 3 ≤ 2 / x – 2
(iv) 5x – 2 / 3 - 7x – 3 / 5 ≥ x/4
(v) 3x + 17 ≤ 2(1 – x)
(vi) 2x+4 ≥ 5/x-1

Q3. Solve the system of inequalities and represent the solutions on the number line.
(i) 5x/4 + 3x/8 > 39/8, 2x–1/12 – x–1/3 ≤ 3x + 1/4
(ii) 2(2x + 3) – 10 ≤ 6 (x – 2), 2x – 3/4 + 6 ≥ 2 + 4x/3
(iii) x/2x+1 ≥ 1/4, 6x/4x-1 ≤ 1/2

Q4. Solve graphically: - (i) 3x + 4y ≥ 12, y ≥ 1, x ≥ 0 (ii) x – 2y ≥ 0, 2x – y ≤ -2, x ≥ 0, y ≥ 0
(iii) 2x+y ≤ 24, x + y ≤ 11, 2x + 5y ≤ 40, x ≥ 0, y ≥ 0

Q5. In first four papers each of 100 marks, Rohit got 72, 83, 73, 95 marks. If he wants an average of greater than or equal to 75 marks and less than 80 marks, find the range of marks he should score in the fifth paper.

Q6. The sum of two natural numbers is 121. If the sum of bigger number and four times the smaller is equal to or greater than 271, find all possible values of the smaller number.

Q7. Given P = {x : 5 ≤ 2x – 1 ≤ 11, x €R} and Q = { x : -1 ≤ 3 + 4x ≤ 23, x €E, x €I} Where R = real numbers and I = integers. Represent P and Q on two different number lines. Write down the elements of P &Q.

Q8. The cost and revenue functions of a product are given by C (x) = 2x + 400 and R(x) = 6x+20 respectively, where x is the number of items produced by the manufacturer. How many items must the manufacturer sell to realize some profit?

Q9. Solve :- - 4x ≥ 30 when (i) x €R (ii) x €Z (iii) x €N

Q10. Solve : 4x – 2 ≤ 8, when :- (i) x €R, (ii) x € Z (iii) x €N

Q11. How many litres of water will have to be added to 1250 litres of 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Q.1 Solve the inequality and show the graph of the solution on number line: 3(1 – x) < 2 (x + 4).

Q.2 IQ of a person is given by the formula iQ = MA/CA x 100
Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.

Q.3 In a game, a person wins if he gets the sum greater than 20 in four throws of a die. In three throws he got numbers 6, 5, 4. What should be his forth throw, so that he wins the game.

Q.4 Solve the inequality - 3 ≤ 4 - 7x/2 ≤ 18

Q.5 A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by f = 9/8 C + 32?

Q.6 Solve 7x + 9 30.

Q.7 Solve the inequality 7 ≤ (3x+11)/2 ≤ 11

Q.8 How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Q.9 Solve 4x + 3 < 6x + 7.

Q.10 Solve 7x + 3 < 5x + 9. Show the graph of the solutions on number line.

Q.11 Solve the system of inequalities : 3x - 7 < 5+x 11 - 5x ≤ 1 and represent the solution on the number line.

Q.12 Solve the following system of inequalities graphically: x + y ≥ 4, 2x – y > 0.

Q.13 Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0.

Q.14 Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1.

Q.15 To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita’s marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade ‘A’ in the course.

Q.16 A shopkeeper sells a product at a price four times more than its actual price. Find the actual price such that the shopkeeper gets a benefit of at least Rs 40.

Q.17 The longest side of the rectangle is five times the shortest side. If the perimeter of the rectangle is atleast 120 cm. Find the minimum value of shortest side.

Q.18 A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

Q.19 Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0.

Q.20 Solve the inequalities and represent the solution graphically on number line: 5x + 1 > –24, 5x – 1 < 24.