$|x+3|-|4-x|=|8+x| \text { How many solutions will this equation have? }$

A. 0

B. 1

C. 2

D. 3

A. 0

Take 4 cases

(i) x < –8
–7 = –x – 8 i.e. x = –1, not satisfies assumed condition.

(ii) –8 < x < –3
–7 = x+8 i.e. x = –15, not satisfies assumed condition

(iii) –3 < x < 4
2x–1 = x + 8 i.e. x = 9, not satisfies assumed condition

(iv) x > 4
7 = x + 8 i.e. x = 1, not satisfied assumed condition

So 0 solution.