Solving inequality with modulus

**Punch** · June 2nd 2011, 11:39 PM

Solve the inequality $(x+2)(x-3)>|2x-1|$

$(x+2)(x-3)>2x-1$ or $(x+2)(x-3)<1-2x$

Solving the first inequality: $x^2-x-6>2x-1$

$x^2-3x-5>0$

$x<-1.19$ or $x>4.19$

Solving the second inequality: $x^2-x-6<1-2x$

$x^2+x-7<0$

$-3.19<x<2.19$

so, $x<-1.19$ or $x>4.19$ or $-3.19<x<2.19$

But the answer is $x<-3.19$ or $x>4.19$

Where did i go wrong? please advise, thanks!

**FernandoRevilla** · June 3rd 2011, 12:15 AM

Originally Posted by Punch

Solve the inequality $(x+2)(x-3)>|2x-1|$

$(x+2)(x-3)>2x-1$ or $(x+2)(x-3)<1-2x$

It should be:

$(x+2)(x-3)>|2x-1|\Leftrightarrow$

$\begin{Bmatrix} (x+2)(x-3)>2x-1 & \mbox{ if }& x\geq 1/2\\(x+2)(x-3)>1-2x & \mbox{if}& x<1/2\end{matrix}$

**Punch** · June 3rd 2011, 12:35 AM

but how would that change my answer?

**HallsofIvy** · June 3rd 2011, 02:37 AM

You found x= -1.19 as a solution to (x+2)(x-3)> 2x-1 but |2x-1|= 2x-1 only if 2x-1>= 0 or x>= 1/2, as FernandoRevilla said. -1.19 is NOT greater than 1/2.

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