Question

How do you solve `\frac { y + 1} { 2} = - 2( y + 1)`?

Answer 1

`y = -1`

Explanation:

First, multiple each side of the equation by `2` to eliminate the fraction which will make the problem easier to work with as well as keeping the equation balanced:

`2 (y + 1)/2 = 2 * -2(y + 1)`

`cancel(2) (y + 1)/cancel(2) = -4(y + 1)`

#y + 1= -4(y + 1)

Next expand the term in parenthesis:

`y + 1 = -4y - 4`

Now perform the necessary mathematics to isolate the `y` terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

`y + 1 - 1 + 4y = -4y - 4 - 1 + 4y`

`y + 4y = -5`

`5y = -5`

Last, divide each side of the equation by `5` to solve for `y` and keep the equation balanced:

`(5y)/5 = (-5)/5`

`(cancel(5)y)/cancel(5) = (-5)/5`

`y = -1`