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

Answer:

$\huge\boxed{No \ solutions}$

Step-by-step 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!