Chapter 4 - Linear Equations in One Variable Exercise Ex. 4(A)

Question 1

State, true or false:

Solution 1

Question 2

State, whether the following statements are true or false:

(i) a < b, then a - c < b - c

(ii) If a > b, then a + c > b + c

(iii) If a < b, then ac > bc

(iv) If a > b, then 

(v) If a - c > b - d, then a + d > b + c

(vi) If a < b, and c > 0, then a - c > b - c

Where a, b, c and d are real numbers and c  0.

Solution 2

(i) a < b  a - c < b - c

The given statement is true.

(ii) If a > b  a + c > b + c

The given statement is true.

(iii) If a < b  ac < bc

The given statement is false.

(iv) If a > b  

The given statement is false.

(v) If a - c > b - d  a + d > b + c

The given statement is true.

(vi) If a < b  a - c < b - c (Since, c > 0)

The given statement is false.

Question 3

If x  N, find the solution set of inequations.

(i) 5x + 3  2x + 18

(ii) 3x - 2 < 19 - 4x

Solution 3

(i) 5x + 3  2x + 18

5x - 2x  18 - 3

3x  15

x  5

Since, x  N, therefore solution set is {1, 2, 3, 4, 5}.

(ii) 3x - 2 < 19 - 4x

3x + 4x < 19 + 2

7x < 21

x < 3

Since, x  N, therefore solution set is {1, 2}.

Question 4

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

(i) x + 7  11

(ii) 3x - 1 > 8

(iii) 8 - x > 5

(iv) 7 - 3x  

(v) 

(vi) 18  3x - 2

Solution 4

(i) x + 7  11

x  11 - 7

x  4

Since, the replacement set = W (set of whole numbers)

Solution set = {0, 1, 2, 3, 4}

(ii) 3x - 1 > 8

3x > 8 + 1

x > 3

Since, the replacement set = W (set of whole numbers)

Solution set = {4, 5, 6, …}

(iii) 8 - x > 5

- x > 5 - 8

- x > -3

x < 3

Since, the replacement set = W (set of whole numbers)

Solution set = {0, 1, 2}

(iv) 7 - 3x  

-3x   - 7

-3x  

x  

Since, the replacement set = W (set of whole numbers)

Solution set = {0, 1, 2}

(v) 

Since, the replacement set = W (set of whole numbers)

Solution set = {0, 1}

(vi) 18  3x - 2

18 + 2  3x

20  3x

Since, the replacement set = W (set of whole numbers)

Solution set = {7, 8, 9, …}

Question 5

Solve the inequation:

3 - 2x  x - 12 given that x  N.

Solution 5

3 - 2x  x - 12

-2x - x  -12 - 3

-3x  -15

x  5

Since, x  N, therefore,

Solution set = {1, 2, 3, 4, 5}

Question 6

If 25 - 4x  16, find:

(i) the smallest value of x, when x is a real number,

(ii) the smallest value of x, when x is an integer.

Solution 6

25 - 4x  16

-4x  16 - 25

-4x  -9

x 

x 

(i) The smallest value of x, when x is a real number, is 2.25.

(ii) The smallest value of x, when x is an integer, is 3.

Question 7

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

Solution 7

Since, the replacement set of real numbers.

Solution set = {x: x  R and }

Since, the replacement set of real numbers.

Solution set = { x: x  R and }

Since, the replacement set of real numbers.

Solution set = { x: x  R and x > 80}

Since, the replacement set of real numbers.

Solution set = { x: x  R and x > 13}

Question 8

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

Solution 8

Thus, the required smallest value of x is -1.

Question 9

Find the largest value of x for which

2(x - 1)  9 - x and x  W.

Solution 9

2(x - 1)  9 - x

2x - 2  9 - x

2x + x  9 + 2

3x  11

Since, x  W, thus the required largest value of x is 3.

Question 10

Solve the inequation:  and x  R.

Solution 10

Solution set = {x: x  R and x  6}

Question 11

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

Solution 11

Since, x  {integers}

Solution set = {-1, 0, 1, 2, 3, 4}

Question 12

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

.

Solution 12

Since, x  {whole numbers}

Solution set = {0, 1, 2, 3, 4}