Inequalities question. No clue how to solve it Watch

Joburger
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This is probably a standard, easy question for most people studying Maths on here so forgive me for asking. I just really need some help. It's been troubling me all day. I just can't get my head around solving inequalities.


The question is:


 | {2x^2-x-6} | > |x|


Can anybody show me how to tackle this, and what answer i should be getting, and how it's worked out. No clue myself :confused: :confused:
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Joburger
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The Modulus sign confuses me especially. Let alone trying to solve the whole thing
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Mr M
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(Original post by Joburger)
This is probably a standard, easy question for most people studying Maths on here so forgive me for asking. I just really need some help. It's been troubling me all day. I just can't get my head around solving inequalities.


The question is:


 | {2x^2-x-6} | > |x|


Can anybody show me how to tackle this, and what answer i should be getting, and how it's worked out. No clue myself :confused: :confused:
Square both sides, rearrange and factorise into the product of two quadratic factors. Job done.
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ztibor
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(Original post by Joburger)
This is probably a standard, easy question for most people studying Maths on here so forgive me for asking. I just really need some help. It's been troubling me all day. I just can't get my head around solving inequalities.


The question is:


 | {2x^2-x-6} | > |x|


Can anybody show me how to tackle this, and what answer i should be getting, and how it's worked out. No clue myself :confused: :confused:
for the LHS
\displaystyle |2x^2-x-6|=\begin {Bmatrix} 2x^2-x-6 & if & 2x^2-x-6>=0 & x<=-3/2 &or & x>=2 \\ -2x^2+x+6 & if & 2x^2-x-6<0 & -3/2<x<2 \end

for the RHS
\displaystyle |x|=\begin {Bmatrix} x & if &x>=0 \\ -x & if & x<0\end

so you have 4 real intervals to solve inequality
1. x<=-3/2
2. -3/2<x<0
3, 0<=x<2
4. x>=2

f.e 1st case : x<=-3/2 so the original eq.
\displaystyle 2x^2-x-6&gt;-x
\displaystyle 2x^2-6&gt;0
\displaystyle x^2&gt;3 \rightarrow |x|&gt;\sqrt{3}
Considering that x<=-3/2, the solution here
\displaystyle x&lt;-\sqrt{3}
......
aso
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