Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 5 - Linear Inequations [Latest edition]

Solve for x in the following in equation, if the replacement set is N<10: 

x + 5 > 11 

Solve for x in the following in equation, if the replacement set is N<10: 

 2x + 1 < 17 

 Solve for x in the following in equation, if the replacement set is N<10: 

3x - 5 < 7 

Solve for x in the following in equation, if the replacement set is N<10:

8 - 3x > 2 

Solve for x in the following in equation, if the replacement set is N<10: 

5 - 2x < 11 

Solve for x in the following in-equation, if the replacement set is R; 

3x >12 

Solve for x in the following in-equation, if the replacement set is R;

 2x - 3 < 7  

Solve for x in the following in-equation, if the replacement set is R; 

3x + 2 ≤ 11 

Solve for x in the following in-equation, if the replacement set is R; 

14 - 3x > 5 

Solve for x in the following in-equation, if the replacement set is R; 

7x + 11 > 16 - 3x 

Solve for x in the following in-equation, if the replacement set is R; 

3x + 25 < 8x - 10 

Solve for x in the following in-equation, if the replacement set is R; 

2(3x - 5) ≤ 8 

Solve for x in the following in-equation, if the replacement set is R; 

x + 7 ≥ 15 + 3x 

Solve for x in the following in-equation, if the replacement set is R; 

2x - 7 ≥  5x + 8

Solve for x in the following in-equation, if the replacement set is R; 

9 - 4x ≤ 15 - 7x 

Solve for x : 6 - 10x < 36, x ∈  {-3, -2, -1, O, 1, 2} 

Solve for x : 3 - 2x ≥ x - 12, x ∈  N 

Solve for x: 5x - 9 ≤ 15 - 7x ,  x ∈ W 

Solve for x : 7 + 5x > x - 13, where x is a negative integer.

Solve for x : 5x - 14 < 18 - 3x, where x ∈  W 

Solve for x : 2x + 7 ≥  5x - 14, where x is a positive prime number. 

Solve for x : `"x"/4 + 3 <= "x"/3 + 4` , where xis a negative odd number.

Solve for x : `("x" + 3)/3 <= ("x" + 8)/4` , where x is a positive even number.

If x + 17 ≤  4x + 9, find the smallest value of x, when:

 x ∈  Z 

If x + 17 ≤  4x + 9, find the smallest value of x, when: 

x ∈ R

If `(2 "x" + 7)/3 <=  (5 "x" +1)/4` , find the smallest value of x, when: 

(i) x ∈ R

(ii) x ∈ Z

Solve the following linear in-equation and graph the solution set on a real number line: 

2x - 11≤ 7 - 3x, x ∈ N 

Solve the following linear in-equation and graph the solution set on a real number line: 

3(5x+ 3) ≥ 2(9x-17), x ∈ W 

Solve the following linear in-equation and graph the solution set on a real number line: 

2(3x-5) > 5(13-2x), x ∈ W 

Solve the following linear in-equation and graph the solution set on a real number line :

3x - 9 ≤ 4x - 7 < 2x + 5,  x ∈  R 

Solve the following linear in-equation and graph the solution set on a real number line: 

2x - 7 < 5x + 2 ≤ 3x + 14, x ∈ R  

Solve the following linear in-equation and graph the solution set on a real number line: 

`-3 <= 1/2 - (2 "x")/3 <= 2 2/3` , x  ∈ N

Solve the following linear in-equation and graph the solution set on a real number line :

`4 3/4 >= "x" + 5/6 > 1/3` , x ∈ R

Solve the following linear in-equation and graph the solution set on a real number line :

`1/3 (2x - 1) < 1/4 (x + 5) < 1/6 (3x + 4)`, x ∈ R

Solve the following linear in-equation and graph the solution set on a real number line: 

`1/3 (5"x" - 8) >= 1/2 (4"x" - 7) `, x ∈ R

Solve the following linear in-equation and graph the solution set on a real number line:

`5/4 "x" > 1 + 1/3 (4"x" - 1)` , x ∈ R

If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines : 

P ∩ Q

If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines: 

Q' ∩ P

If P = { x : -3 < x ≤ 7, x ∈ R} and Q = { x : - 7 ≤ x < 3, x ∈ R} , represent the following solution set on the different number lines: 

P-Q 

If P = {x : 7x - 2 > 4x + 1, x ∈  R} and Q = {x : 9x - 45 ≥  5 (x -5),x ∈ R} , represent the following solution set on different number lines: 

P ∩ Q

If P = {x : 7x - 2 > 4x + 1, x ∈  R} and Q = {x : 9x - 45 ≥  5 (x -5),x ∈ R} , represent the following solution set on different number lines: 

P - Q

If P = {x : 7x - 2 > 4x + 1, x ∈  R} and Q = {x : 9x - 45 ≥  5 (x -5),x ∈ R} , represent the following solution set on different number lines: 

P ∩ Q'

If P = {x : 7x - 4 > 5x + 2, x ∈  R} and Q - {x : x - 19 ≥ 1 - 3x, x ∈ R}, represent the following solution set on different number lines: 

P ∩ Q

If P = {x : 7x - 4 > 5x + 2, x ∈  R} and Q - {x : x - 19 ≥ 1 - 3x, x ∈ R}, represent the following solution set on different number lines: 

P' ∩ Q