VeritasPrepKarishma wrote:
gmatpapa wrote:
Which of the following represents the complete range of x over which x^3 - 4x^5 < 0?
(A) 0 < |x| < ½
(B) |x| > ½
(C) –½ < x < 0 or ½ < x
(D) x < –½ or 0 < x < ½
(E) x < –½ or x > 0
Responding to a pm:
The problem is the same here.
How do you solve this inequality: \((1+2x)*x^3*(1-2x)<0\)
Again, there are 2 ways -
The long algebraic method: When is \((1+2x)*x^3*(1-2x)\) negative? When only one of the terms is negative or all 3 are negative. There will be too many cases to consider so this is painful.
The number line method: Multiply both sides of \((1+2x)*x^3*(1-2x)<0\) by -1 to get \((2x + 1)*x^3*(2x - 1)>0\)
Take out 2 common to get \(2(x + 1/2)*x^3*2(x - 1/2)>0\) [because you want each term to be of the form (x + a) or (x - a)]
Now plot them on the number line and get the regions where this inequality holds.
Basically, you need to go through this entire post:
inequalities-trick-91482.htmlResponding to a pm:
Quote:
Why we meed to multiply the both sides by -1? What if the question is x^3 ( 2x+1) ( 1-2x )<0 or >0 do
we need in this caee to multiply the both sides by -1?
We need to bring the factors in the (x - a)(x - b) format instead of (a - x) format.
So how do you convert (1 - 2x) into (2x - 1)? You multiply by -1.
Say, if you have 1-2x < 0, and you multiply both sides by -1, you get -1*(1 - 2x) > (-1)*0 (note here that the inequality sign flips because you are multiplying by a negative number)
-1*(1 - 2x) > (-1)*0
-1 + 2x > 0
(2x -1) > 0
So you converted the factor to x - a form.
In case you have x^3 ( 2x+1) ( 1-2x )<0, you will multiply both sides by -1 to get
x^3 ( 2x+1) ( 2x - 1 ) > 0 (inequality sign flips)
_________________
Karishma
Veritas Prep GMAT Instructor
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