Question

C. ax + bx = 10

I need help, I am going into HS and don't understand how to solve this. This is summer HW

Answer 1

10/a+b=x

Explanation:

Divide both sides by a+b

Answer 2

`x=(10)/(a+b)` with
`a \\eq -b`.

Explanation:

So we have:

`ax+bx=10` and we are solving for
`x`.

We want to get all terms that have x on one side and all terms without x on the opposing side. This is actually already done.

Now we are going to factor the side that has the x's. We are going to factor x out.

`x(a+b)=10`

Now you have a number times x and you want x by itself. The inverse operation of multiplication is division. So we are going to divide both sides by
`(a+b)`:

`x=(10)/(a+b)`

You could probably stop here but just in case....

`a+b` can't be 0 because then you would have 10/0 which is not a number.

So if we solve
`a+b=0` we can find out what we don't want and b to be:

`a+b=0`

Subtract b on both sides:

`a=-b`

So we we don't want
`a` and
`-b` to be the same value.