## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Ex 4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Ex 4

Question 1.

Solve the inequation 3x – 11 < 3 where x ∈ {1, 2, 3,……, 10}. Also, represent its solution on a number line

Solution:

Question 2.

Solve 2(x – 3) < 1, x ∈ {1, 2, 3, …. 10}

Solution:

Question 3.

\(E=mc^2\)

Solve 5 – 4x > 2 – 3x, x ∈ W. Also represent its solution on the number line.

Solution:

Question 4.

List the solution set of 30 – 4 (2x – 1) < 30, given that x is a positive integer.

Solution:

Question 5.

Solve : 2 (x – 2) < 3x – 2, x ∈ { – 3, – 2, – 1, 0, 1, 2, 3} .

Solution:

Question 6.

If x is a negative integer, find the solution set of \(\\ \frac { 2 }{ 3 } \)+\(\\ \frac { 1 }{ 3 } \) (x + 1) > 0.

Solution:

Question 7.

Solve: \(\frac { 2x-3 }{ 4 } \ge \frac { 1 }{ 2 }\), x ∈ {0, 1, 2,…,8}

Solution:

Question 8.

Solve x – 3 (2 + x) > 2 (3x – 1), x ∈ { – 3, – 2, – 1, 0, 1, 2, 3}. Also represent its solution on the number line.

Solution:

Question 9.

Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9} solve x – 3 < 2x – 1.

Solution:

Question 10.

Given A = {x : x ∈ I, – 4 ≤ x ≤ 4}, solve 2x – 3 < 3 where x has the domain A Graph the solution set on the number line.

Solution:

Question 11.

List the solution set of the inequation

\(\\ \frac { 1 }{ 2 } \) + 8x > 5x \(– \frac { 3 }{ 2 } \), x ∈ Z

Solution:

Question 12.

List the solution set of \(\\ \frac { 11-2x }{ 5 } \) ≥ \(\\ \frac { 9-3x }{ 8 } \) + \(\\ \frac { 3 }{ 4 } \), x ∈ N

Solution:

Question 13.

Find the values of x, which satisfy the inequation : \(-2\le \frac { 1 }{ 2 } -\frac { 2x }{ 3 } \le 1\frac { 5 }{ 6 } \), x ∈ N. Graph the solution set on the number line. (2001)

Solution:

Question 14.

If x ∈ W, find the solution set of

\(\frac { 3 }{ 5 } x-\frac { 2x-1 }{ 3 } >1\)

Also graph the solution set on the number line, if possible.

Solution:

Question 15.

Solve:

(i)\(\frac { x }{ 2 } +5\le \frac { x }{ 3 } +6\) where x is a positive odd integer.

(ii)\(\frac { 2x+3 }{ 3 } \ge \frac { 3x-1 }{ 4 } \) where x is positive even integer.

Solution:

Question 16.

Given that x ∈ I, solve the inequation and graph the solution on the number line:

\(3\ge \frac { x-4 }{ 2 } +\frac { x }{ 3 } \ge 2 \) (2004)

Solution:

Question 17.

Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9}, find the values of x for which -3 < 2x – 1 < x + 4.

Solution:

Question 18.

Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N

Solution:

Question 19.

If x ∈ Z, solve 2 + 4x < 2x – 5 ≤ 3x. Also represent its solution on the number line.

Solution:

Question 20.

Solve the inequation = 12 + \(1 \frac { 5 }{ 6 } x\) ≤ 5 + 3x, x ∈ R. Represent the solution on a number line. (1999)

Solution:

Question 21.

Solve: \(\\ \frac { 4x-10 }{ 3 } \)≤\(\\ \frac { 5x-7 }{ 2 } \) x ∈ R and represent the solution set on the number line.

Solution:

Question 22.

Solve \(\frac { 3x }{ 5 } -\frac { 2x-1 }{ 3 } \) > 1, x ∈ R and represent the solution set on the number line.

Solution:

Question 23.

Solve the inequation – 3 ≤ 3 – 2x < 9, x ∈ R. Represent your solution on a number line. (2000)

Solution:

Question 24.

Solve 2 ≤ 2x – 3 ≤ 5, x ∈ R and mark it on a number line. (2003)

Solution:

Question 25.

Given that x ∈ R, solve the following inequation and graph the solution on the number line: -1 ≤ 3 + 4x < 23. (2006)

Solution:

Question 26.

Solve tlie following inequation and graph the solution on the number line. (2007)

\(-2\frac { 2 }{ 3 } \le x+\frac { 1 }{ 3 } <3+\frac { 1 }{ 3 } \) , x ∈ R

Solution:

Question 27.

Solve the following inequation and represent the solution set on the number line:

\(-3<-\frac { 1 }{ 2 } -\frac { 2x }{ 3 } \le \frac { 5 }{ 6 } ,x\in R\)

Solution:

Question 28.

Solve \(\frac { 2x+1 }{ 2 } +2(3-x)\ge 7,x\in R\). Also graph the solution set on the number line

Solution:

Question 29.

Solving the following inequation, write the solution set and represent it on the number line. – 3(x – 7) ≥ 15 – 7x > \(\\ \frac { x+1 }{ 3 } \), n ∈ R

Solution:

Question 30.

Solve the inequation :

\(-2\frac { 1 }{ 2 } +2x\le \frac { 4x }{ 3 } \le \frac { 4 }{ 3 } +2x,\quad x\in W\). Graph the solution set on the number line.

Solution:

Question 31.

Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line. (2011)

Solution:

Question 32.

If x ∈ I, A is the solution set of 2 (x – 1) < 3 x – 1 and B is the solution set of 4x – 3 ≤ 8 + x, find A ∩ B.

Solution:

Question 33.

If P is the solution set of -3x + 4 < 2x – 3, x ∈ N and Q is the solution set of 4x – 5 < 12, x ∈ W, find

(i) P ∩ Q

(ii) Q – P.

Solution:

Question 34.

A = {x : 11x – 5 > 7x + 3, x ∈ R} and B = {x : 18x – 9 ≥ 15 + 12x, x ∈ R}

Find the range of set A ∩ B and represent it on a number line

Solution:

Question 35.

Given: P {x : 5 < 2x – 1 ≤ 11, x ∈ R)

Q {x : – 1 ≤ 3 + 4x < 23, x ∈ I) where

R = (real numbers), I = (integers)

Represent P and Q on number line. Write down the elements of P ∩ Q. (1996)

Solution:

Question 36.

If x ∈ I, find the smallest value of x which satisfies the inequation \(2x+\frac { 5 }{ 2 } >\frac { 5x }{ 3 } +2\)

Solution:

Question 37.

Given 20 – 5 x < 5 (x + 8), find the smallest value of x, when

(i) x ∈ I

(ii) x ∈ W

(iii) x ∈ N.

Solution:

Question 38.

Solve the following inequation and represent the solution set on the number line:

\(4x-19<\frac { 3x }{ 5 } -2\le -\frac { 2 }{ 5 } +x,x\in R\)

Solution:

Question 39.

Solve the given inequation and graph the solution on the number line:

2y – 3 < y + 1 ≤ 4y + 7; y ∈ R.

Solution:

Question 40.

Solve the inequation and represent the solution set on the number line.

\(-3+x\le \frac { 8x }{ 3 } +2\le \frac { 14 }{ 3 } +2x,Where\quad x\in I\)

Solution:

Question 41.

Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.

Solution:

Question 42.

One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres. Find the length of the shortest pole.

Solution: