Question

How do you evaluate `\frac { a } { 7} + \frac { 5} { 7} = \frac { 3} { 7}`?

Answer 1

`a=-2`

Explanation:

As all the denominators (bottom numbers) are the same it is equally true to write:

`a+5=3`

A purist would have said: multiply both sides by 7
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now consider: `a+5=3`

Subtract `color(red)(5)` from both sides

`color(green)(a+5=3 color(white)("dddd")->color(white)("dddd")a+5color(red)(-5)color(white)("d")=color(white)("d")3color(red)(-5))`

`color(green)(color(white)("dddddddddddd")->color(white)("dddd")a+color(white)("d")0color(white)("d")=color(white)("d")-2`

`color(green)( color(white)("dddddddddddd")-> color(white)("dddd") acolor(white)("dddd.d")=color(white)("d")-2)`