Question

The sum of -7 times a number and 8 times the sum of the number and 1 is the same as the number minus 7.

Answer 1

`\huge\boxed{No \ solutions}`

Explanation:

Our first goal is to transform these words into numbers for an expression.

Let's break it down.

-7 times a number

We'll assume that the number is
`n`. -7 times a number can be represented as
`-7n`.

8 times the sum of the number and 1

We can break this complex statement down.

8 times the sum of the number and 1

The sum of the number and 1 will be
`n+1`. 8 times that will be
`8(n+1)`. Since it says at the beginning the sum of, we add
`8(n+1)` to
`-7n`.

`-7n + 8(n+1)`

Is the same as the number minus 7.

"Is the same" means we use an equal sign. The number minus 7 will be
`n-7`. So we get
`-7n + 8(n+1)=n-7`

Now we can solve for n by reversing the equation until we have n isolated on one side.

`-7n + 8n + 8 = n-7`

`n + 8 = n-7`

`8 = -7`

We end up with 8 = -7. This is not possible. Therefore, there are no real values of x that satisfy this equation.

Hope this helped!