Question

Show step by step for equation -8/3x + 4(x + 9/4) = -2/3(x + 12/8) + 3

Answer 1

The value of x in the given equation is
`-(13)/(3)`

That is
`x=(-13)/(3)`

Explanation:

Given equation is
`(-8)/(3)x+4(x+(9)/(4))=(-2)/(3)(x+(12)/(8))+3`

To simply the given equation as below :

`(-8)/(3)x+4(x+(9)/(4))=(-2)/(3)(x+(12)/(8))+3`

`(-8)/(3)x+4(x+(9)/(4))=(-2)/(3)(x+4)+3`

`(-8)/(3)x+4x+9=(-2)/(3)x+((-2)/(3))(4)+3` ( applying the distributive property )

`(-8)/(3)x+4x+9=(-2)/(3)x+((-2)/(3))(4)+3`

`(-8)/(3)x+4x+9=(-2)/(3)x+(-8)/(3)+3`

`(-8x+12x)/(3)+9=(-2)/(3)x+(-8+9)/(3)`

`(4x)/(3)+9=(-2)/(3)x+(1)/(3)`

`(4x)/(3)+9-((-2)/(3)x+(1)/(3))=(-2)/(3)x+(1)/(3)-((-2)/(3)x+(1)/(3))`

`(4x)/(3)+9+(2)/(3)x-(1)/(3)=0`

`(6x)/(3)+9-(1)/(3)=0`

`(6x+27-1)/(3)=0`

`(6x+26)/(3)=0`

6x+26=0

6x=-26

`x=-(26)/(6)`

`x=-(13)/(3)`

Therefore the value of x is
`-(13)/(3)`

That is
`x=(-13)/(3)`