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

1 Answer
Mar 21, 2018

#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)#