Question

How do you solve `1+ \frac { 1} { x - 7} = \frac { 4x } { x - 7}`?

Answer 1

`x = -2`

Explanation:

`1 + 1/(x-7) = (4x)/(x-7)`

Subtract `1/(x-7)` from both sides of the `=` sign.

`1 = (4x)/(x-7) - 1/(x-7)`

Since both of the right side fractions have the same denominator `(x-7)`, the subtraction of the second from the first can be written as:

`1 = (4x-1)/(x-7)`

Now you can multiply both sides by `x-7`.

`1(x-7) = 4x-1`

Multiply out the bracket.

`x-7 =4x-1`

Subtract `x` from both sides:

`-7 = 3x - 1`

Add `1` to both sides.

`-6 = 3x`

Divide both sides by `3`.

`-2 = x`