Absolute Value

[vabrol]

if |x/3|>1 , which of the following must be true

1) x>3

2) x

3)x=3

4)x3

5)x

 

OA:

4, shouldn't it be 5

 

 

Please explain.

[jmbamba]

|x/3|=|x|/|3|=|x|/3.

 

Thus, if |x/3|>1, then |x|/3 >1 and |x|>3.

 

The only convenient answer choice is D, x3.

Choice E "x3 but x >-3.

[SmallFish]

Just to extend on the same lines,

 

|x/3|>1, x/3>1 or -x/3>1, x>3 or -x>3, x>3 or x

 

So any value of x should satisfy x>3 and x

 

1) does not satisfy x

2) does not satisfy x>3

3) does not satisfy either

4) satisfies both

5) does not satisfy x>3

[Raj1972]

Just to extend on the same lines,

 

|x/3|>1, x/3>1 or -x/3>1, x>3 or -x>3, x>3 or x

 

So any value of x should satisfy x>3 and x

 

1) does not satisfy x

2) does not satisfy x>3

3) does not satisfy either

4) satisfies both

5) does not satisfy x>3

 

 

|x/3|>1, x/3>1 or -x/3>1, x>3 or -x>3, x>3 or x is is x>3 or x 3 or x

[asur]

x >3 or -x > 3 ==> x > 3 or (-1) (-x) > (-1) (3) ==> x> 3 or x

You just change the equality sign when you multiply by -ve number on both sides...

[SmallFish]

|x/3|>1, x/3>1 or -x/3>1, x>3 or -x>3, x>3 or x is is x>3 or x 3 or x

 

You are right, i missed the -ve sign :-) Rest of my answer holds good though :-)