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hi, apply definition absolute value obtain two possibilites: A. if x≥0 then 0<|x|-4x<5 go 0<x-4x<5 go 0<-3x<5, go 0>x>-5/3. The intersection is empty B. if x<0 then 0<|x|-4x<5 go 0<-x-4x<5 go 0<-5x<5 go 0>x>-1. the intersection is -1<x<0

Got to the correct answer but took too much time...E

If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

0<|x|-4x<5 = ?

A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer.

Got to the correct answer but took too much time...E

If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

0<|x|-4x<5 = ?

A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer.

I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!

Got to the correct answer but took too much time...E

If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

0<|x|-4x<5 = ?

A. x<0 B. 0<x<1 C. -3/5<x<1 D. -3/5<x<0 E. -1<x<0

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out. If x = 1/2, |x|-4x is negative so B and C are out. If x = -4/5, |x|-4x = 4 so D is out and E is the answer.

I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!

Focus on "and if there is even one value outside the given range that does satisfy the inequality, it is not the answer." given above.

-4/5 is a value which satisfies 0 < |x|-4x < 5 since |-4/5|-4(-4/5) = 4. Since -4/5 does not lie in the range -3/5<x<0 so (D) cannot be the answer. The correct range needs to cover all possible values of x.

There are two options here - plugging in values given to us in the answer choices or simplifying the inequality.

0<|x|-4x<5

x>0: 0<x-4x<5 0<-3x<5 0<x<-5/3 -5/3<x<0 INVALID as x does not fall within the range of x>0 OR x<0: 0<(-x)-4x<5 0<-5x<5 0<x<-1 -1<x<0 VALID as x falls within the range of x<0

Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]
29 Jan 2014, 20:03

Expert's post

jlgdr wrote:

Would be happy to hear some comments on whether this approach is correct

|x|-4x>0

So we have two cases

If x>0 then x-4x>0 -3x>0 x<0, this contradicts and hence is not a valid solution

If x<0 then -5x>0 x<0, this solution is valid

So we get that -1<x<0 replacing in the original inequality

E

Knowing only x < 0, how do you choose between (A), (D) and (E)? You need to consider |x| - 4x < 5 too When x < 0, -x -4x < 5 -5x < 5 x > -1 That's how you get -1 < x < 0

Or work on the whole inequality in one go 0 < |x| - 4x < 5 When x < 0, 0< -x - 4x < 5 0 < -5x < 5 0 < -x < 1 0 > x > -1