Question

Question #82ba7

Answer 1

`x=-4`

Explanation:

Use the method of `color(blue)"cross- multiplying"`

`"Given " a/b=c/d" then"`

`•color(white)(xx) ad=bc`

`rArr3/(x+1)=5/(x-1)`

`rArr5(x+1)=3(x-1)`

distributing gives.

`5x+5=3x-3`

`"subtract 3x from both sides"`

`5x-3x+5=cancel(3x)cancel(-3x)-3`

`rArr2x+5=-3`

`"subtract 5 from both sides."`

`2xcancel(+5)cancel(-5)=-3-5`

`rArr2x=-8`

`"divide both sides by 2"`

`(cancel(2) x)/cancel(2)=(-8)/2`

`rArrx=-4`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side equals the right side then it is the solution.

`"left side " =3/(-4+1)=3/(-3)=-1`

`"right side " =5/(-4-1)=5/(-5)=-1`

`rArrx=-4" is the solution"`