Ncert Solutions For Class 8 Maths Ex 2.3

Ncert Solutions For Class 8 Maths Chapter 2 Ex 2.3

Question 1:

Solve and check. 3x = 2x + 18.

Solution:

3X = 2X + 18

Transpose 2x to L.H.S,

3x – 2x = 18   →   [ x = 18 ]

L.H.S :  3X   → (3 x 18) = 54

R.H.S :  2X + 18  → (2 X 18) + 18

→ 36 + 18 = 54

L.H.S = R.H.S

Hence proved.

 

Question 2:

Solve and check. 5x + 9 = 5 + 3x

Solution:

5x – 3x = 5 – 9

2x =  -4

Dividing 2 by both sides,

x  =  -2

L.H.S :  5X + 9 →  5 X  (-2) + 9

→  -10 + 9  =    -1

R.H.S :  5 + 3X  →  5 +  3 X (-2)

→ 5 – 6  = -1

L.H.S   =   R.H.S

Hence proved.

 

Question 3:

Solve and check. 4z + 3 = 6 + 2z.

Solution:

4z + 3 = 6 + 2z

Transpose 2z to left hand side   &  3 to right hand side.

4z – 2z   =   6 – 3

2z  =  3  →    z  = (3÷2)

L.H.S :    4z + 3    =    4 x (3÷2)+ 3

→  (12÷2)  + 3   →  6 + 3  =    9

R.H.S :     6 + 2z  = 6 + 2  x (3÷2)

→ 6 + (6÷2)

→ 6 + 3 =   9

L.H.S    =    R.H.S

Hence proved.

 

Question 4:

Solve and check. x = (4÷5) (x  + 10)

Solution:

X =  (4÷5) ( X + 10)

Multiply 5 on both sides

5x = 4(x + 10) → 5x = 4x + 40

Transpose 4x to L.H.S,

5X – 4X = 40.  →  X  =  40

L.H.S :        X   =  40

R.H.S :   (4÷5) ( X + 10)    →   (4÷5) ( 40 + 10)

(4÷5) X  50 = 40

L.H.S    =   R.H.S

Hence proved.

 

Question 5:

Solve and check.  2x/3+1=7x/15+3

Solution:

2x/3+1=7x/15+3

Transpose 7x / 15   to  L.H.S

Transpose    1  to  R.H.S

2x / 3  –  7x / 15   =   3 – 1

5  X 2x – 7x / 15  = 2

3x / 15 = 2 →      x /5  = 2

→    x /5  = 2  multiply 5 on both sides  .

X = 10

L.H.S  = 2x / 3  + 1 =  2 x 10 / 3   + 1

=2×10+1×3÷3

= 23÷3

R.H.S  = =7x÷15+3=7×10÷15+3

= 7×2÷3+3=14÷3+3

=14+3×3÷3

=23÷3

L.H.S  =  R.H.S

Hence proved.

 

Question 6:

Solve and check.  2y + 5/3 = 26 / 3 – y.

Solution:

2Y  + 5/3 = 26/3 – Y

Transpose y to L.H.S.

Transpose 5/3 to R.H.S.

2y + y  = 26/3  –  5/3

3y = 21/3    (i.e)  3y = 7

Divide 3 by both sides,

→    y = 7/3

L.H.S :

2Y = 5/3        =  2 X 7/3 + 5/3     = 14/3 + 5/3     =  19/3

R.H.S :

26/3 – y          =  26/3 – 7/3              =  19/3

L.H.S = R.H.S

Hence proved.

 

Question 7:

Solve and check. 3m = 5m – (8÷5)

Solution:

3m -5m = – (8÷5)

-2m =  – (8÷5)

Divide -2 on both sides,

m = (4÷5)

L.H.S :

3m = 3 x (4÷5)

=  (12÷5)

R.H.S :

= 5M – (8÷5)

= 5 X(4÷5)  –– (8÷5)

= (12÷5)

L.H.S = R.H.S

Hence proved.

 

Question 8:

Solve and check. 5g – 3 = 3g – 5

Solution:

Transpose 3t to L.H.S.

Transpose -3 to R.H.S.

5g – 3g = -5 – (-3)

2g = -2

Divide 2 on both sides,

g = -1

L.H.S :

5g – 3      =   5 x (-1) -3                 = -5-3       = -8

R.H.S :

3g – 5      = 3 x (-1) -5                    = -3 -5    = -8

L.H.S  = R.H.S

Hence proved

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