Question

How do you solve `-4( k + 5) = - 4k - 17`?

Answer 1

`"no solution"`

Explanation:

`"distribute the bracket"`

`-4k-20=-4k-17`

`"add 4k to both sides"`

`cancel(-4k)cancel(+4k)-20=cancel(-4k)cancel(+4k)-17`

`rArr-20=-17larrcolor(blue)"which is false"`

`"hence the equation has no solution"`

Answer 2

There are no solutions

Explanation:

`-4(k + 5)=-4k - 17`
Distribute the left side
`(-4)(k)+(-4)(5) = -4k - 17`
`-4k - 20 = -4k - 17`
Add `color(red)(20)` to both sides
`-4k - 20 + color(red)(20) = -4k - 17 + color(red)(20)`
`-4k = -4k + 3`
Then,
Add `4k` to both sides
`-4k + 4k = -4k + 3 + 4k`
`0=3`

Hence,
There are no solutions