INEQUATION

EXERCISE - A

1) Study each of the following carefully and write the Range of the following:

a)

b)

c)

EXERCISE - B

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

a) x+ 7≤ 11.

b) 3x - 1> 8.

c) 8- x > 5

d) 7 - 3x ≥ -1/2.

e) x- 3/2 < 3/2 - x.

f) 18≤ 3x -2.

g) x+2> 5.

h) 3x -7 ≤ 1.

i) x -1 < 4 - x.

j) 5x+3 < 2x +8.

k) x +1/2 ≥ 3x +11/4.

l) x/3 - 2/3 > x/2 - 3/2.

EXERCISE - C

1) Represent the following inequalities on real number lines:

a) x>3.

b) 2x -1<5.

c) 3x+1≤-5.

d) 3x -2 ≥ -8.

e) 5x < 1.

f) 2(2x -3)≤ 6.

g) -4< x < 4.

h) -2≤ x < 5.

i) 8≥ x > -3.

j) -5< x ≤ 1.

EXERCISE - D

1) Solve the inequations

a) 4x -1> x +11.

b) 7 - x ≤ 2- 6x.

c) x+3 ≤ 2x +9.

d) 2 - 3x > 7 -5x

e) 1+ x ≥ 5x -11.

f) (2x+5)/3 > 3x -3.

EXERCISE -E

1) Solve the INEQUATION of the following:

a) 30- 2(4x -1)> -8; x ∈ (positive integers)

b) 2(x+1)+ 3(2x -1)>15; x ∈ (2,3,4,5)

c) 2(x-2)+ 3(x -3)≤ 2; x ∈ (positive integers)

d) 4(x+3) - 5(x +2)>0 ; x ∈ (positive integers)

2) If the replacement set ={-5,-3,-2,-1,0,1,2,3}, list the solution set of 3x -2< 2.

3) List the solution set of 25 -4(2x -1)< 25, x∈N.

4) If the replacement set is {-2,-1,1,2,4,5,9}, what is the solution set of each of the following mathematical sentences ?

a) x+ 3/2 > 5/2.

b) x -4 = -3.

c) 2x -5 ≥ 10.

d) 3x +2 ≤ 5/2.

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

6) If 20- 5x < 5(x+8), find the smallest value of x, when

i) x ∈Z 

ii) x ∈ W.

iii) x ∈ N.

7) Answer True or False:

i) If x+10= y+ 14, then x > y.

ii) If 10- x > 3, then x <7.

iii) If x= y+2, then x > y.

iv) If a and b are natural numbers such that a < b, then 1/a < 1/b.

v) 3 ∈ {x : 3x -2≥ 5}.

vi) If a> b and c> 0, then AC > bc.

vii) If a> b and c <0, then ac < bc.

viii) If a > b, then a² > b².

8) If x is a negative integer, find the solution set of 2/7 + 1/7  (x +1)> 0.

9) If x ∈ W, solve, 5x - 4< 6x -10.

10) If x ∈ N, solve, (x -1)/2 ≤ (x+5)/3.

11) x ∈ Z, solve, 2/3 > 4 + (2- 5x)/4.

12) If x ∈ N, solve, (5x -6)/(2x +3) < 2.

13) Find the truth set of the inequality x > y+2, where

(x, y) ∈ {(1,2), (2,3), (5,1),(7,3), (5,6),(6,5).

14) Solve 3(x -2)≥ 2x -3. Hence draw a graph using a number line.

15) Solve: (x -2)/(2x +4) < 1/3, Hence draw a diagram using number line for this inequation.

16) Translate the following sentences into open sentences:

a) 3 more than 4 times a number.

b) 3 less than one-third a number.

c) father's age is 15 years. greater than 2 times his son's age.

d) A number and its reciprocal equals to 3.