Problem: If x<−2 then ∣1−∣1+x∣∣ equals
Answer Choices:
A. 2+x
B. −2−x
C. x
D. −x
E. −2
Solution:
By definition
∣a∣={a​a≥0−a​a<0​
If x<−2, then 1+x<0 and 11+x+=−(1+x) and ∣1−∣1+x∣∣=∣1+1+x∣=∣2+x∣. Again if x<−2, then 2+x<0 and ∣2+x∣=−2−x.