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

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

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

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

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

State, whether the following statements are true or false:

a < b, then a – c < b – c

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

If a < b, then ac > bc.

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

If a – c > b – d; then a + d > b + c

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

If x ∈ N, find the solution set of inequations.

5x + 3 ≤ 2x + 18

If x ∈ N, find the solution set of inequations.

3x – 2 < 19 – 4x

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

x + 7 ≤ 11

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

3x – 1 > 8

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

8 – x > 5

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

`7 - 3x >= - 1/2`

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

`x  - 3/2 < 3/2 - x`

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

18 ≤ 3x – 2

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

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

`5 + x/4 > x/5 + 9`

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

`(x + 3)/8 < (x - 3)/5`

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.

Solve the inequation:

`12 + 1 5/6 x ≤ 5 + 3x` and `x in R`.

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

–5 ≤ 2x – 3 < x + 2

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

–1 ≤ 3 + 4x < 23

Represent the following inequalities on real number line:

2x – 1 < 5

Represent the following inequalities on real number line:

3x + 1 ≥ – 5

Represent the following inequalities on real number line:

2(2x – 3) ≤ 6

Represent the following inequalities on real number line:

– 4 < x < 4

Represent the following inequalities on real number line:

– 2 ≤ x < 5

Represent the following inequalities on real number line:

8 ≥ x > – 3

Represent the following in-equalities on real number line :

−5 < × ≤ −1

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

x – 1 < 3 – x ≤ 5

Represent the solution of the following inequalities on the real number line:

4x – 1 > x + 11

Represent the solution of the following inequalities on the real number line:

7 – x ≤ 2 – 6x

Represent the solution of the following inequalities on the real number line:

x + 3 ≤ 2x + 9

Represent the solution of the following inequalities on the real number line:

2 – 3x > 7 – 5x

Represent the solution of the following inequalities on the real number line:

1 + x ≥ 5x – 11

Represent the solution of the following inequalities on the real number line:

`(2x + 5)/3 > 3x - 3`

x ∈ {real numbers} and –1 < 3 – 2x ≤ 7, evaluate x and represent it on a number line.

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

Solve and graph the solution set of:

5 > p – 1 > 2 or 7 ≤ 2p – 1 ≤ 17, p ∈ R

The diagram represents two inequations A and B on real number lines:

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

Use the real number line to find the range of values of x for which:

x > 3 and 0 < x < 6

Use the real number line to find the range of values of x for which:

x < 0 and –3 ≤ x < 1

Use the real number line to find the range of values of x for which:

–1 < x ≤ 6 and –2 ≤ x ≤ 3

Illustrate the set {x : –3 ≤ x < 0 or x > 2; x ∈ R} on the real number line.

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

P is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45 ≥ 5(x – 5); where x ∈ R. Represent:

1. P ∩ Q
2. P – Q
3. P ∩ Q’ on the different number of lines.

If P = {x : 7x – 4 > 5x + 2, x ∈ R} and Q = {x : x – 19 ≥ 1 – 3x, x ∈ R}; find the range of set P ∩ Q and represent it on a number line.

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.

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

`3 >= (x - 4)/2 + x/3 >= 2`

Given:

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 the number line.

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 given inequation and graph the solution on the number line.

2y – 3 < y + 1 ≤ 4y + 7, y ∈ R

Solve the inequation:

3z – 5 ≤ z + 3 < 5z – 9, z ∈ R.

Graph the solution set on the number line.

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

`-3 < -1/2 - (2x)/3 ≤ 5/6, x ∈ R`

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 following in equation, write the solution set and represent it on the number line:

`-"x"/3≤ "x"/2 -1 1/3<1/6, "x" in "R"`

Find the values of x, which satify the inequation

-2`5/6 < 1/2 - (2"x")/3 ≤ 2, "x" in "W"`

Graph the solution set on the number line.

Solve the following in equation and write the solution set:

13x - 5 < 15x + 4 < 7x + 12, x ∈ R

Represent the solution on a real number line.

Solve the following inequation, write the solution set and represent it on the number line.

`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`

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

`-8 1/2 < -1/2 - 4x ≤ 7 1/2, x ∈ I`