• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details

Chapter 8: Linear Equations in One Variable Exercise – 8.1

Question: 1

Verify by substitution that:

(i) x = 4 is the root of 3x – 5 = 7

(ii) x = 3 is the root of 5 + 3x = 14

(iii) x = 2 is the root of 3x – 2 = 8x – 12

(iv) x = 4 is the root of 3x/2 = 6

(v) y = 2 is the root of y – 3 = 2y – 5

(vi) x = 8 is the root of (1/2)x + 7 = 11

Solution:

(i) x = 4 is the root of 3x - 5 = 7.

Now, substituting x = 4 in place of ‘x’ in the given equation 3x - 5 = 7,

3(4) – 5 = 7

12 – 5 = 7

7 = 7

Since, LHS = RHS

Hence, x = 4 is the root of 3x - 5 = 7.

(ii). x = 3 is the root of 5 + 3x = 14.

Now, substituting x = 3 in place of ‘x’ in the given equation 5 + 3x = 14,

5 + 3(3) = 14

5 + 9 = 14

14 = 14

Since, LHS = RHS

Hence, x = 3 is the root of 5 + 3x = 14.

(iii). x = 2 is the root of 3x – 2 = 8x – 12.

Now, substituting x = 2 in place of ‘x’ in the given equation 3x –2 = 8x – 12,

3(2) – 2 = 8(2) – 12

6 – 2 = 16 – 12

4 = 4

Since, LHS = RHS

Hence, x = 2 is the root of 3x – 2 = 8x – 12.

(iv) x = 4 is the root of 3x/2 = 6.

Now, substituting x = 4 in place of ‘x’ in the given equation 3x/2 = 6,

(3× 4)/2 = 6

12/2 = 6

6 = 6

Since, LHS = RHS

Hence, x = 4 is the root of 3x/2 = 6.

(v). y = 2 is the root of y – 3 = 2y – 5.

Now, substituting y = 2 in place of ‘y’ in the given equation y – 3 = 2y – 5,

2 – 3 = 2(2) – 5

-1 = 4 – 5

-1 = -1

Since, LHS = RHS

Hence, y = 2 is the root of y – 3 = 2y – 5.

(vi). x = 8 is the root of 12x + 7 = 11.

Now, substituting x = 8 in place of ‘x’ in the given equation 12x + 7 = 11,

12(8) + 7 =11

4 + 7 = 11

11 = 11

Since, LHS = RHS

Hence, x = 8 is the root of 12x + 7 = 11.

 

Question: 2

Solve each of the following equations by trial and error method:

(i) x + 3 = 12

(ii) x – 7 = 10

(iii) 4x = 28

(iv) x/2 + 7 = 11

(v) 2x + 4 = 3x

(vi) x/4 = 12

(vii) 15/x = 3

(viii) x/18 = 20

Solution:

(i) x + 3 = 12

Here, LHS = x + 3 and RHS = 12


	
		
	
	

		

			
x
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
1
			
1 + 3 = 4
			
12
			
No
		
		

			
2
			
2 + 3 = 5
			
12
			
No
		
		

			
3
			
3 + 3 = 6
			
12
			
No
		
		

			
4
			
4 + 3 = 7
			
12
			
No
		
		

			
5
			
5 + 3 = 8
			
12
			
No
		
		

			
6
			
6 + 3 = 9
			
12
			
No
		
		

			
7
			
7 + 3 = 10
			
12
			
No
		
		

			
8
			
8 + 3 = 11
			
12
			
No
		
		

			
9
			
9 + 3 = 12
			
12
			
Yes
		
	




Therefore, if x = 9, LHS = RHS.

Hence, x = 9 is the solution to this equation.

(ii) x – 7 = 10

Here, LHS = x – 7 and RHS = 10.


	
		
	
	

		

			
x
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
9
			
9 – 7 = 2
			
10
			
No
		
		

			
10
			
10 – 7 = 3
			
10
			
No
		
		

			
11
			
11 – 7 = 4
			
10
			
No
		
		

			
12
			
12 – 7 = 5
			
10
			
No
		
		

			
13
			
13 – 7 = 6
			
10
			
No
		
		

			
14
			
14 – 7 = 7
			
10
			
No
		
		

			
15
			
15 – 7 = 8
			
10
			
No
		
		

			
16
			
16 – 7 = 9
			
10
			
No
		
		

			
17
			
17 – 7 = 10
			
10
			
Yes
		
	




Therefore, if x = 17, LHS = RHS.

Hence, x = 17 is the solution to this equation.

(iii) 4x = 28

Here, LHS = 4x and RHS = 28.




	
		
	
	

		

			
x
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
1
			
4 x 1 = 4
			
28
			
No
		
		

			
2
			
4 x 2 = 8
			
28
			
No
		
		

			
3
			
4 x 3 = 12
			
28
			
No
		
		

			
4
			
4 x 4 = 16
			
28
			
No
		
		

			
5
			
4 x 5 = 20
			
28
			
No
		
		

			
6
			
4 x 6 = 24
			
28
			
No
		
		

			
7
			
4 x 7 = 28
			
28
			
Yes
		
	


Therefore, if x = 7, LHS = RHS

Hence, x = 7 is the solution to this equation.

(iv) x/2 + 7 = 11

Here, LHS = x/2 + 7 and RHS = 11.

Since RHS is a natural number, x/2 must also be a natural number, so we must substitute values of x that are multiples of 2.


	
		
	
	

		

			
x
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
2
			
2/2 + 7 = 8
			
11
			
No
		
		

			
4
			
4/2 + 7 = 9
			
11
			
No
		
		

			
6
			
6/2 + 7 = 10
			
11
			
No
		
		

			
8
			
8/2 + 7 = 11
			
11
			
Yes
		
	


Therefore, if x = 8, LHS = RHS.

Hence, x = 8 is the solution to this equation.

(v) 2x + 4 = 3x

Here, LHS = 2x + 4 and RHS = 3x.


	
		
	
	

		

			
x
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
1
			
2(1) + 4 = 6
			
3(1) = 3
			
No
		
		

			
2
			
2(2) + 4 = 8
			
3(2) = 6
			
No
		
		

			
3
			
2(3) + 4 =10
			
3(3) = 9
			
No
		
		

			
4
			
2(4) + 5 = 12
			
 3(4) = 12
			
Yes
		
	




Therefore, if x = 4, LHS = RHS.

Hence, x = 4 is the solution to this equation.

(vi) x/4 = 12

Here, LHS = x/4 and RHS = 12.

Since RHS is a natural number, x/4 must also be a natural number, so we must substitute values of x that are multiples of 4.


	
		
	
	

		

			
X
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
16
			
16/4 = 4
			
12
			
No
		
		

			
20
			
20/4 = 5
			
12
			
No
		
		

			
24
			
24/4 = 6
			
12
			
No
		
		

			
28
			
28/4 = 7
			
12
			
No
		
		

			
32
			
32/4 = 8
			
12
			
No
		
		

			
36
			
36/4 = 9
			
12
			
No
		
		

			
40
			
40/4 = 10
			
12
			
No
		
		

			
44
			
44/4 = 11
			
12
			
No
		
		

			
48
			
48/4 = 12
			
12
			
Yes
		
	


Therefore, if x = 48, LHS = RHS.

Hence, x = 48 is the solution to this equation.

(vii) 15x = 3

Here, LHS = 15x and RHS = 3.

Since RHS is a natural number, 15x must also be a natural number, so we must substitute values of x that are factors of 15.


	
		
	
	

		

			
x
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
1
			
15/1= 15
			
3
			
No
		
		

			
3
			
15/3 = 5
			
3
			
No
		
		

			
5
			
15/5 = 3
			
3
			
Yes
		
	


Therefore, if x = 5, LHS = RHS.

Hence, x = 5 is the solution to this equation.

(viii) x/18 = 20

Here, LHS = x/18 and RHS = 20.

Since RHS is a natural number, x/18 must also be a natural number, so we must substitute values of x that are multiples of 18.


	
		
	
	

		

			
X
			
LHS
			
RHS
			
Is LHS = RHS
		
		

			
324
			
324/18 = 18
			
20
			
No
		
		

			
342
			
342/18 = 19
			
20
			
No
		
		

			
360
			
360/18 = 20
			
20
			
Yes
		
	


Therefore, if x = 360, LHS = RHS.

Hence, x = 360 is the solution to this equation.

• Complete AIPMT/AIIMS Course and Test Series
• OFFERED PRICE: Rs. 15,900


• View Details Xpress Buy

Course Features

• 728 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution