Set the inputs 0.5k-5 and k+7 equal to each other. Then solve for k
0.5k-5 = k+7
0.5k-5-0.5k = k+7-0.5k
-5 = 0.5k+7
-5-7 = 0.5k+7-7
-12 = 0.5k
0.5k = -12
0.5k/0.5 = -12/0.5
k = -24
So if k = -24, then the expressions 0.5k-5 and k+7 will be equal to each other. What will they be equal to? Let's find out
k+7 = -24+7 = -17
0.5*k-5 = 0.5*(-24)-5 = -12-5 = -17
Both inputs will be equal to -17 if k = -24
The relation B = {(0.5k-5, 10), (k+7, 4)} will update to B = {(-17, 10), (-17, 4)} when k = -24. This relation is NOT a function due to the fact the input x = -17 leads to more than one output (y = 10 and y = 4 at the same time).
