Question

How do you solve `2(x-1) + 3= x -3(x+1)`?

Answer 1

`x=-1`

Explanation:

`"distribute brackets on both sides of the equation"`

`2x-2+3=x-3x-3`

`"simplify both sides"`

`2x+1=-2x-3`

`"add 2x to both sides"`

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

`rArr4x+1=-3`

`"subtract 1 from both sides"`

`4xcancel(+1)cancel(-1)=-3-1`

`rArr4x=-4`

`"divide both sides by 4"`

`(cancel(4) x)/cancel(4)=(-4)/4`

`rArrx=-1`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left "=2(-2)+3=-4+3=-1`

`"right "=-1-3(0)=-1`

`rArrx=-1" is the solution"`

Answer 2

`x=-1`

Explanation:

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

Open the brackets from both the sides

`2x-2+3=x-3x-3`

Bring all `x` terms on one side and the other terms on the other side

`2x-x+3x=2-3-3`

`4x=-4`

`x=(-4)/4`

`x=-1`