First, convert each mixed number into an improper fraction:

#2 5/12 = -3 1/4 + k#

#2 + 5/12 = -(3 + 1/4) + k#

#(12/12 xx 2) + 5/12 = -([4/4 xx 3] + 1/4) + k#

#24/12 + 5/12 = -(12/4 + 1/4) + k#

#29/12 = -13/4 + k#

Next, add #color(red)(13/4)# to each side of the equation to isolate #k# while keeping the equation balanced:

#color(red)(13/4) + 29/12 = color(red)(13/4) - 13/4 + k#

#13/4 + 29/12 = 0 + k#

#13/4 + 29/12 = k#

Then, we need to put #13/4# over a common denominator so we can add the two fractions by multiplying it by an appropriate form of #1#:

#(3/3 xx 13/4) + 29/12 = k#

#39/12 + 29/12 = k#

#68/12 = k#

Now, if necessary we can convert the improper fraction back into a mixed number:

#60/12 + 8/12 = k#

#5 + (4 xx 2)/(4 xx 3) = k#

#5 + (color(red)(cancel(color(black)(4))) xx 2)/(color(red)(cancel(color(black)(4))) xx 3) = k#

#5 + 2/3 = k#

#5 2/3 = k#

#k = 5 2/3#