Solving checking the linear equation

Question

6(x-7) - 7 (x- 6) = x +6 - (x-5)?

Answer 1

Given  equation is  6 (  x - 7 ) - 7 (  x - 6 )  =  x + 6 - (  x - 5 )

        Multiply   in  the  equation   6 x - 42  - 7 x + 42  =  x + 6  - x  +  5

                                                     6 x  -  7 x  =  11 

                                                     - x  =  11

                                                       x   =  - 11

The  Solution  is  x = - 11

Answer 2

Given  6(x - 7) - 7(x - 6) = x + 6 - (x - 5)

Distribute the terms using distributive law: a(b - c) = ab - ac

6*x - 6*7 - 7*x + 7*6 = x + 6 - x + 5 { product of same signs is positive }

6x - 42 - 7x + 42  = x + 6 - x + 5

6x - 7x = 6 + 5

-x = 11

Multiply with "-" sign on each side

x = -11

CHECKING :

Substitute x = -11 in the given expression

6( -11 - 7) - 7(-11 - 6) = -11 +  6 - (-11 - 5)

6(-18) - 7(-17) = -5 - (-16)

-108 + 119 = -5 + 16

11 = 11

L . H .S = R .H .S

Therefore x = -11