Question

Solve the equation-5y-9=-(y-1)

Answer 1

`-2 (1)/(2)`

Explanation:

So, we have


`-5y-9=-(y-1)`
The first thing we need to do is distribute, which makes


`-5y-9=-y+1`

Then, we add 9 to both sides to get rid of the 9 on the left side of the equation, leaving -5y alone


`-5y=-y+10`

After that, we must remove the y on the right side by adding y to both
sides. Since y is defined as 1, unless said otherwise, we will be left with


`-4y=10`
Now, this is where it can get a little confusing. At this point, all that's left to do is divide -4y by 4, and 10 by 4, which will give us


`(-4y)/(-4) = (10)/(-4)`

`y = (10)/(-4)`

This should be the end of the equation, but we need to simplify it to get our final answer. Since 4 and 10 both share 2 as a common factor, we will use 2 to simplify our fraction, which leaves us with


`-(5)/(2)`

But we still aren't done! Since the numerator is a higher number than the denominator, this is considered an improper fraction, which means we must convert it into a mixed number fraction.

We take the devisor, in this case, 2, and divide it by 5.


`-5` ÷
`-2=-2`
`r1`

This leaves us with 2, and a remainder of one. Since the denominator stays the same, this will leave us with a final answer of


`-2(1)/(2)`

Answer 2

As given by the question

There are given that the equation:

`-5y-9=-(y-1)`

Now,

Solve the above equation

So,

`\begin{gathered} -5y-9=-(y-1) \\ -5y-9=-y+1 \\ -5y-9+y-1=0 \\ -4y-10=0 \end{gathered}`

Then,

`\begin{gathered} -4y-10=0 \\ -4y=10 \\ y=(10)/(-4) \\ y=-2.5 \end{gathered}`

Hence, the value of y is -2.5.