Which inequalities have no solution? Check all of the boxes that apply. A. x > x B. –3x mr001-1.jpg –3x C. –4 + x > –2 + x D. x – 2 < x + 3

Question

asked Jul 1, 2019 122k views

2 Answers

Maxpolk · Answer 1 · 2019-07-07T13:19:22+0000

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

$x>x\\\\\Rightarrow x-x>0\\\\\Rightarrow 0>1,$

which cannot be possible, so this inequality will have no solution.

(B) We have

$-3x=-3x\\\\\Rightarrow -3x+3x=0\\\\\Rightarrow 0=0,$

which is always true, so this equation will have infinitely many solutions.

(C) We have

$-4+x>-2+x\\\\\Rightarrow -4+x+2-x>0\\\\\Rightarrow -2>0,$

which is never true, so this inequality will have no solution.

(D) We have

$x-2<x+3\\\\\Rightarrow x-2-x-3<0\\\\\Rightarrow -5<0,$

which is always true, so this inequality will have infinitely many solutions.

Thus, the correct options are (A) and (C).