MATH SOLVE

4 months ago

Q:
# Which inequalities have no solution? Check all of the boxes that apply. A. x > xB. –3x mr001-1.jpg –3xC. –4 + x > –2 + xD. x – 2 < x + 3

Accepted Solution

A:

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).

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).