Answer :
Answer: The answer is (A) and (C).
Step-by-step explanation: We are given four options and we are to check which of these inequalities have no solution.
(A) We have
[tex]x>x\\\\\Rightarrow x-x>0\\\\\Rightarrow 0>1,[/tex]
which cannot be possible, so this inequality will have no solution.
(B) We have
[tex]-3x=-3x\\\\\Rightarrow -3x+3x=0\\\\\Rightarrow 0=0,[/tex]
which is always true, so this equation will have infinitely many solutions.
(C) We have
[tex]-4+x>-2+x\\\\\Rightarrow -4+x+2-x>0\\\\\Rightarrow -2>0,[/tex]
which is never true, so this inequality will have no solution.
(D) We have
[tex]x-2<x+3\\\\\Rightarrow x-2-x-3<0\\\\\Rightarrow -5<0,[/tex]
which is always true, so this inequality will have infinitely many solutions.
Thus, the correct options are (A) and (C).
