How many integer solutions are there to the inequality |x + 8|

Question

How many integer solutions are there to the inequality  |x+8|<x ?

A. 0

B. 2

C. 3

D. 8

E. 16

Bunuel · Accepted Answer

How many integer solutions are there to the inequality  |x+8|<x ?
 
A. 0
B. 2
C. 3
D. 8
E. 16

x cannot be negative because a negative number, x, cannot be greater than the non-negative value of |x + 8|.

x cannot be 0, because |0 + 8| = 8, and 8 is not less than 0.

For positive x, since x + 8 > 0, we'd have |x + 8| = x + 8. Thus, when x is positive, the inequality becomes x + 8 < x, which simplifies to 8 < 0, which is not correct. Therefore, for positive x, the inequality also does not have a solution.

Answer: A.

Showmeyaa · Answer

|x+8|<x 
-x < x + 8 < x
-x - 8 < x < x - 8
-8 < x < -8
IMO, A = 0

SouravShrivastava · Answer

Draw graph of |x+8| & x separately.....
You will see |x+8| is always greater than x...
Thus for no value of x x>|x+8|
Ans is 0.

kaladin123 · Answer

Posting the graph just in case someone's wondering what it looks like.
 https://i.ibb.co/khsSP2Q/plot.jpg 
Source:  Wolfram Alpha

PRamesh2008 · Answer

Here is another way of solving this problem..

Hope this helps..

PrinceDAYAL · Answer

Hello  Bunuel ,

Can you please post the solution to this question?

unraveled · Answer

How many integer solutions are there to the inequality  |x+8|<x ?

A. 0

B. 2

C. 3

D. 8

E. 16

|x+8|<x  means that x will always be positive

Testing values of x
x = 1, then  |x+8|<x  does not make sense as 9 < 1 is not possible.
x = 5, then too  |x+8|<x  does not make sense as 13 < 5 is not possible.

We can also see that LHS will always be 8 greater than RHS.

Thus, this inequality stands invalid i.e. x has not integer values as solution.

Answer A.

How many integer solutions are there to the inequality |x + 8| < x?

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