Selina solutions for Concise Mathematics [English] Class 10 ICSE chapter 4 - Linear Inequations (In one variable) [Latest edition]

If x ∈ W, then the solution set of the inequation −x > −7, is ______.

The value of x, for 4(2x – 5) < 2x + 28, x ∈ R is ______.

The solution set for the inequation – 2x + 7 ≤ 3, x ∈ R is ______.

For 7 – 3x < x – 5, the solution is ______.

x(8 – x) > 0 and x ∈ N gives ______.

State, true or false:

`x < -y => -x > y`

State, true or false:

`-5x >= 15 => x >= -3`

State, true or false:

`2x <= -7 => (2x)/(-4) >= (-7)/(-4)`

State, true or false:

`7 > 5 => 1/7 < 1/5`

State whether the following statement is true or false:

If a < b, then a – c < b – c

State whether the following statement is true or false:

If a > b, then a + c > b + c

State whether the following statement is true or false:

If a < b, then ac > bc.

State whether the following statement is true or false:

If a > b, then `a/c < b/c`                           

State whether the following statement is true or false:

If a – c > b – d; then a + d > b + c

State whether the following statement is true or false:

If a < b, and c > 0, then a – c > b – c where a, b, c and d are real numbers and c ≠ 0.

Solve the inequation:

3 – 2x ≥ x – 12 given that x ∈ N.

If 25 – 4x ≤ 16, find:

1. the smallest value of x, when x is a real number.
2. the smallest value of x, when x is an integer.

If the replacement set is the set of real numbers, solve:

– 4x ≥ – 16

If the replacement set is the set of real numbers, solve:

8 – 3x ≤ 20

Find the smallest value of x for which `5 - 2x < 5 1/2 - 5/3x`, where x is an integer.

Find the largest value of x for which 2(x – 1) ≤ 9 – x and x ∈ W.

For the following real number line, the solution set is:

The solution set for the following number line is:

The following number line represents:

The solution set for the following number line is:

The number line for the solution of inequation x > 5 and x < 10 (x ∈ R) is:

For graph given alongside, write an inequation taking x as the variable:

For graph given alongside, write an inequation taking x as the variable:

For graph given alongside, write an inequation taking x as the variable:

For graph given alongside, write an inequation taking x as the variable:

For the following inequations, graph the solution set on the real number line:

– 4 ≤ 3x – 1 < 8

For the following inequation, graph the solution set on the real number line:

–1 < 3 – 2x ≤ 7

For the following inequations, graph the solution set on the real number line:

x – 1 < 3 – x ≤ 5

List the elements of the solution set of the inequation –3 < x – 2 ≤ 9 – 2x; x ∈ N.

Find the range of values of x which satisfies

`-2 2/3 <= x + 1/3 < 3 1/3, x in R`

Graph these values of x on the number line.

Find the values of x which satisfy the inequation:

`-2 <= 1/2 - (2x)/3 ≤ 1 5/6; x ∈ N`

Graph the solution on the number line.

Given x ∈ {real numbers}, find the range of values of x for which –5 ≤ 2x – 3 < x + 2 and represent it on a number line.

If 5x – 3 ≤ 5 + 3x ≤ 4x + 2, express it as a ≤ x ≤ b and then state the values of a and b.

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

2x – 3 < x + 2 ≤ 3x + 5, x ∈ R

Solve and graph the solution set of:

2x – 9 < 7 and 3x + 9 ≤ 25, x ∈ R

Solve and graph the solution set of:

2x – 9 ≤ 7 and 3x + 9 > 25, x ∈ I

Solve and graph the solution set of:

x + 5 ≥ 4(x – 1) and 3 – 2x < –7, x ∈ R

Solve and graph the solution set of:

3x – 2 > 19 or 3 – 2x ≥ – 7, x ∈ R

The diagrams represent two inequations A and B on real number lines:

A =

B =

1. Write down A and B in set builder notation.
2. Represent A ∩ B and A ∩ B' on two different number lines.

Given A = {x: –1 < x ≤ 5, x ∈ R} and B = {x: – 4 ≤ x < 3, x ∈ R}

Represent on different number lines:

A ∩ B

Given A = {x : –1 < x ≤ 5, x ∈ R} and B = {x : – 4 ≤ x < 3, x ∈ R}

Represent on different number lines:

A' ∩ B

Given A = {x : –1 < x ≤ 5, x ∈ R} and B = {x : – 4 ≤ x < 3, x ∈ R}

Represent on different number lines:

A – B

Find the range of values of x, which satisfy:

`- 1/3 <= x/2 + 1 2/3 < 5 1/6`

Graph in each of the following cases the values of x on the different real number lines:

1. x ∈ W
2. x ∈ Z
3. x ∈ R

Given: A = {x : –8 < 5x + 2 ≤ 17, x ∈ I}, B = {x : –2 ≤ 7 + 3x < 17, x ∈ R}

Where R = {real numbers} and I = {integers}. Represent A and B on two different number lines. Write down the elements of A ∩ B.

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

The maximum value of x (x ∈ Z) for the inequation 4x ≤ 12 + x is ______.

The minimum value of x (x ∈ Z) for the inequation 5x – 4 ≥ 18 – 6x is ______.

If 1 ≤ −x < 5, x is an integer then the sum of smallest and greatest values of x is ______.

The value of x for the inequation 3x + 15 < 5x + 13, x ∈ Z is ______.

The real number lines for two inequations A and B are as given below, A ∩ B is:

For the inequations A and B [as given above in part (e)], A ∪ B is:

`-3/2 ≥ -(2x)/3` where x ∈ R.

Assertion (A): The largest value of x is `9/4`.

Reason (R): When the signs of both the sides of an inequation are changed, the sign of inequality reverses.

Inequation 5 − 2x ≥ x − 10, where x ∈ N (natural numbers)

Assertion (A): 5 − 2x ≥ x − 10
⇒ −3x ≥ −15 ⇒ x ≥ 5
∴ Solution set = {5, 6, 7, 8, ........}

Reason (R): 5 − 2x ≥ x − 10 ⇒ 5 + 10 ≥ 5
⇒ x ≤ 5
∴ Solution set = {1, 2, 3, 4, 5}

x ∈ W, x ≥ −3 and x < 5. 

Statement (1): There will be no solution for the given inequations.

Statement (2): The real the given inequations is:

5  + x  ≤  2x < x − 2, x ∈ R.

Statement (1): There is no value of x ∈ R that satisfies the given inequation. 

Statement (2): 5 + x − x ≤ 2x − x < x − 2 − x 

⇒ 5 ≤ x < −2

Solve the inequation:

`12 + 1 5/6 x ≤ 5 + 3x` and `x in R`.

Given x ∈ {whole numbers}, find the solution set of:

–1 ≤ 3 + 4x < 23

Find the set of values of x, satisfying:

`7x + 3 >= 3x - 5` and `x/4 - 5 <= 5/4 -x`, where x ∈ N

Solve:

`x/2 + 5 <= x/3 + 6`, where x is a positive odd integer

Solve:

`(2x + 3)/3 >= (3x - 1)/4`, where x is a positive even integer

Solve the inequation:

`-2 1/2 + 2x <= (4x)/5 <= 4/3 + 2x, x ∈ W`.

Graph the solution set on the number line.

Find three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of third is at most 20.

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

`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R`

Find the greatest value of x ∈ Z, so that: −1 ≤ 3 + 4x < 23

If 7 ≥ −2x + 1 > −7; find the sum of greatest and smallest values of x ∈ I.

A teacher asked Rohan to draw a triangle with the following condition: The longest side of the triangle is 7 cm less than twice the shortest side and the third side is 7 cm shorter than the longest side. The perimeter of the triangle is at least 84 cm.

Based on the above information, form a linear inequation and answer the following questions:

1. What is the minimum length of the shortest side? 
2. What is the minimum length of the longest side? 
3. Identify the type of triangle that Rohan has drawn along with the length of the possible sides he got. 
4. What is the least area of the triangle drawn?