Question

Verify a(b-c)=ab-ac for a=1.6;b=1/-2;& c=-5/-7​

Answer 1

Given:

`a=1.6,b=(1)/(-2),c=(-5)/(-7)`

To verify:

`a(b-c)=ab-ac` for the given values.

Solution:

We have,

`a=1.6,b=(1)/(-2),c=(-5)/(-7)`

We need to verify
`a(b-c)=ab-ac`.

Taking left hand side, we get

`a(b-c)=1.6\left((1)/(-2)-(-5)/(-7)\right)`

`a(b-c)=1.6\left(-(1)/(2)-(5)/(7)\right)`

Taking LCM, we get

`a(b-c)=1.6\left((-7-10)/(14)\right)`

`a(b-c)=(16)/(10)\left((-17)/(14)\right)`

`a(b-c)=(8)/(5)\left((-17)/(14)\right)`

`a(b-c)=-(68)/(35)\right)`

Taking right hand side, we get

`ab-ac=1.6* (1)/(-2)-1.6* (-5)/(-7)`

`ab-ac=-(16)/(20)-(8)/(7)`

`ab-ac=-(4)/(5)-(8)/(7)`

Taking LCM, we get

`ab-ac=(-28-40)/(35)`

`ab-ac=(-68)/(35)`

Now,

`LHS=RHS`

Hence proved.