Question

Can someone help me with this question

Answer 1

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

Explanation:

Simplify each equation by combining like terms, and then factoring

`(2)/(3) x + (1)/(3) - (1)/(3) x`

=
`(1)/(3) x + (1)/(3)`

=
`(1)/(3)` ( x + 1)

`(4)/(3)x - (4)/(3) - (2)/(3)`

=
`(4)/(3)x - (6)/(3)`

=
`(4)/(3)` ( x - 1 )

`\ ( (1)/(3) x + (2)/(3) ) + ( -(2)/(3)x - (4)/(3))`

=
`-(1)/(3)x - (2)/(3)`

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

`\ ((2)/(3)x + (1)/(3) ) + ((2)/(3) x - (2)/(3) )`

=
`\ (4)/(3)x - (1)/(3)`

=
`\((1)/(3)` ( 4x - 1)

Answer 2

Explanation:

`1)(2)/(3)x + (1)/(3)-(1)/(3)x = (2)/(3)x-(1)/(3)x +(1)/(3)\\\\\\=((2-1))/(3)x+(1)/(3)\\\\\\=(1)/(3)x+(1)/(3)\\\\\\=(1)/(3)(x+1)`

`2) (4)/(3)x-(2)/(3)-(2)/(3)=(4)/(3)x + ((-2-2))/(3)\\\\\\`

`=(4)/(3)x -(4)/(3)\\\\\\=(4)/(3)(x-1)`

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

`= (-1)/(3)x-(2)/(3)\\\\\\=(-1)/(3)(x+2)\\`

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

`=(4)/(3)x-(1)/(3)\\\\\\=(1)/(3)(4x-1)`