Question

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

Answer 1

A. x > x

C. –4 + x > –2 + x

Explanation:

Answer 2

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).