ML Aggarwal solutions for Understanding ICSE Mathematics [English] Class 10 chapter 4 - Linear Inequations [Latest edition]

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

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

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

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

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

If x is a negative integer, find the solution set of `(2)/(3) + (1)/(3)` (x + 1) > 0.

Solve: `(2x - 3)/(4) ≥ (1)/(2)`, x ∈ {0, 1, 2,…,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.

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

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.

List the solution set of the inequation `(1)/(2) + 8x > 5x -(3)/(2)`, x ∈ Z

List the solution set of `(11 - 2x)/(5) ≥ (9 - 3x)/(8) + (3)/(4)`, x ∈ N

Find the values of x, which satisfy the inequation : `-2 ≤ (1)/(2) - (2x)/(3) ≤ 1(5)/(6)`, x ∈ N. Graph the solution set on the number line.

If x ∈ W, find the solution set of `(3)/(5)x - (2x - 1)/(1) > 1` Also graph the solution set on the number line, if possible.

`x/(2) + 5 ≤ x/(3) + 6` where x is a positive odd integer.

`(2x + 3)/(3) ≥ (3x - 1)/(4)` where x is positive even integer.

Given that x ∈ I, solve the inequation and graph the solution on the number line: `3 ≥ (x - 4)/(2) + x/(3) ≥ 2`

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

Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N

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

Solve the inequation = 12 + `1(5)/(6)` ≤ 5 + 3x, x ∈ R. Represent the solution on a number line.

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

Solve `(3x)/(5) - (2x - 1)/(3)` > 1, x ∈ R and represent the solution set on the number line.

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

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

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

Solve the following inequation and graph the solution on the number line. `-2(2)/(3) ≤ x + (1)/(3) < 3 + (1)/(3)`x∈R

Solve the following inequation and represent the solution set on the number line : `-3 < -(1)/(2) - (2x)/(3) ≤ (5)/(6), x ∈ "R"`

Solve `(2x + 1)/(2) + 2(3 - x) ≥ 7, x ∈ "R"`. Also graph the solution set on the number line

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

Solve the inequation : `-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`. Graph the solution set on the number line.

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

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.

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.

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

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. 

If x ∈ I, find the smallest value of x which satisfies the inequation `2x + (5)/(2) > (5x)/(3) + 2`

Given 20 – 5 x < 5 (x + 8), find the smallest value of x, when
(i) x ∈ I
(ii) x ∈ W
(iii) x ∈ N.

Solve the following inequation and represent the solution set on the number line : `4x - 19 < (3x)/(5) - 2 ≤ -(2)/(5) + x, x ∈ "R"`

Solve the given inequation and graph the solution on the number line : 2y – 3 < y + 1 ≤ 4y + 7; y ∈ R.

Solve the inequation and represent the solution set on the number line. `-3 + x ≤ (8x)/(3) + 2 ≤ (14)/(3) + 2x, "Where" x ∈ "I"`

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.

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.

If x ∈ { – 3, – 1, 0, 1, 3, 5}, then the solution set of the inequation 3x – 2 ≤ 8 is

If x ∈ W, then the solution set of the inequation 3x + 11 ≥ x + 8 is

If x ∈ W, then the solution set of the in equation 5 – 4x ≤ 2 – 3x is ______.

If x ∈ I, then the solution set of the inequation 1 < 3x + 5 ≤ 11 is

If x ∈ R, the solution set of 6 ≤ – 3 (2x – 4) < 12 is ______.

Solve the inequation : 5x – 2 ≤ 3(3 – x) where x ∈ { – 2, – 1, 0, 1, 2, 3, 4}. Also represent its solution on the number line.

Solve the inequation:

6x – 5 < 3x + 4, x ∈ I

Find the solution set of the inequation x + 5 < 2 x + 3 ; x ∈ R Graph the solution set on the number line.

If x ∈ R (real numbers) and – 1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.

Solve the inequation : `(5x + 1)/(7) - 4 (x/7 + 2/5) ≤ 1(3)/(5) + (3x - 1)/(7), x ∈ "R"`

Find the range of values of a, which satisfy 7 ≤ – 4x + 2 < 12, x ∈ R. Graph these values of a on the real number line.

If x∈R, solve `2x - 3 ≥ x + (1 - x)/(3) > (2)/(5)x`

Find positive integers which are such that if 6 is subtracted from five times the integer then the resulting number cannot be greater than four times the integer.

Find three smallest consecutive natural numbers such that the difference between one-third of the largest and one-fifth of the smallest is at least 3