How many different values of positive integer x, for which |x+8|

Question

How many different values of positive integer x, for which  |x+8|<x , are there?

A. 0
B. 2
C. 3
D. 8
E. 16

BrushMyQuant · Accepted Answer

|x+8| |1+8| < 8 => 9 < 8 which is NOT true. As, there are all positive signs in the equation so any greater value of x will also not satisfy this equation => Answer will be 0 So, Answer will be A Method 2: Algebra - Reducing the equation |x+8|= 0 => x+8 < x => 8 < 0 Now, this can never be true as 8 > 0 => There are no positive integer values of x which satisfy this equation => Answer will be 0 So, Answer will be A Method 3: Algebra - General Way As we have |x+8| in the equation so we will have two cases - Case 1: x + 8 ≥ 0 => x+8>= 0 => x >= -8 => |x+8| = x+8 (as |X| = X when X >= 0) => x+8 < x => 8 < 0 which is NOT TRUE => NO SOLUTION in this case - Case 2: x + 8 ≤ 0 => x+8 ≤ 0 => x ≤ -8 => |x+8| = -(x+8 ) (as |X| = -X when X < 0) => -(x+8) < x => x + x > -8 => 2x > -8 => x > -4 But the condition was x ≤ -8 => NO SOLUTION in this case But, we are asked about positive values => Answer will be 0 So, Answer will be A Hope it helps! Playlist on Solved Problems on Absolute Values here Watch the following video to learn how to Solve Inequality + Absolute value Problems https://www.youtube.com/watch?v=236auvH8agc

sherxon · Answer

How many different values of positive integer x, for which |x+8|<x, are there?

Let's take the condition as given, that is x>0
for any positive integer x, x+k (k>0) is always greater than x itself.
So there is no values that satisfy the criteria in the question.

Answer is A

chanandler_bong · Answer

Hello, what if the positive x constraint was not there ( hence x can be negative of positive or 0 ). Would there still be 0 values that satisfy the inequality, right ? 
Thank you in advance

Bunuel · Answer

Yes, |x + 8| < x has no solutions even without that constraint.

piyushnagre99 · Answer

The solution provided by you is spot on.

But the Case-2 mentioned in your Method-3 seems to be incorrect as:
x < -8 will still not satisfy the equation
Kindly verify

BrushMyQuant · Answer

piyushnagre99  : Thank you, solution updated. Cheers.

How many different values of positive integer x, for which |x+8|<x

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As we have \|x+8\| in the equation so we will have two cases
-Case 1: x + 8 ≥ 0 => x+8>= 0 => x >= -8 => \|x+8\| = x+8 (as \|X\| = X when X >= 0) => x+8 < x => 8 < 0 which is NOT TRUE => NO SOLUTION in this case	-Case 2: x + 8 ≤ 0 => x+8 ≤ 0 => x ≤ -8 => \|x+8\| = -(x+8 ) (as \|X\| = -X when X < 0) => -(x+8) < x => x + x > -8 => 2x > -8 => x > -4 But the condition was x ≤ -8 => NO SOLUTION in this case

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