how do i find inequalities that has no solutions

Question

Which of these inequalities has no solution A. √x > - 17 B. √x > 17 C. √x < 17 D √x < -17

Answer 1

nun av em

unless yu limit the sq root tu the POSITIV part oenlee

for reel numbers, yu normally get 2 ansers such as x & -x

that kuver -infinity thru + infinity=all reel numbers

Answer 2

In inequality, real numbers are dealt with, imaginary or complex numbers are excluded because those numbers are not real: incomparable.  

Thus, x≧0  and √x≧0 because if x＜0, √x will be the imaginary or complex.

A. √x＞-17: √x≧0, so √x＞-17   Thus, A is solvable.   

The set of solutions, in interval notation, is the interval [ 0, (+)infinity ).

B. √x＞17: Since both sides of the inequality is positive, we can square them.  

We have: x＞289   Thus, B is solvable.   The set of solutions is the interval ( 289, (+)infinity ).

C. √x＜17: This can be restated: 0≦√x＜17   Square both ends and the middle of inequality.          

We have: 0≦x＜289   Thus, C is solvable.   The set of solutions is the interval [ 0, 289 )

D. √x＜-17: This disagrees with the condition: √x≧0.   Thus, D has no solutions.  

The set of solutions is empty.

Therefore, the answer is D that has no solutions.