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Verified Answer :

Solve the mixed fraction first,
\(-2\frac{1}{2} +k =-2 \frac{5}{7}\)
2 x 2 + 1 = 5
7 x 2 + 5 =19
New fraction would be,
\(-\frac{5}{2}\) + k = \(- \frac{19}{7}\)
Solve for k,
k =  \(-\frac{19}{7} + \frac{5}{2}\)
add fraction, by making one denominator
k = \(\frac{-38+35}{14}\)
k=\(- \frac{3}{14}\)
Thus, k = \(- \frac{3}{14}\)