−2∣5w−7∣+9=−7 what is the 2 answers for this question

The two possible answers are w = 3 and w = -1/5

These answers can be obtained through solving to the absolute value symbols. 

−2∣5w−7∣+9=−7 ---> subtract 9 from both sides
−2∣5w−7∣= -16 ---> divide both sides by -2
∣5w−7∣= 8

Now, because of the absolute value symbols, set the inside equal to 8 and -8 for the two answers. 

5w - 7 = 8
5w = 15
w = 3

AND

5w - 7 = -8
5w = -1
w = -1/5