First, factor the fraction on the left side of the equation:

#(7 xx -7)/(7 xx 1) = (a + 7)/6#

#(color(red)(cancel(color(black)(7))) xx -7)/(color(red)(cancel(color(black)(7))) xx 1) = (a + 7)/6#

#-7/1 = (a + 7)/6#

#-7 = (a + 7)/6#

Next, multiply each side of the equation by #color(red)(6)# to eliminate the fraction while keeping the equation balanced:

#color(red)(6) xx -7 = color(red)(6) xx (a + 7)/6#

#-42 = cancel(color(red)(6)) xx (a + 7)/color(red)(cancel(color(black)(6)))#

#-42 = a + 7#

Now, subtract #color(red)(7)# from each side of the equation to solve for #a# while keeping the equation balanced:

#-42 - color(red)(7) = a + 7 - color(red)(7)#

#-49 = a + 0#

#-49 = a#

#a = -49#