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#
