# Math Help - Solving inequality with modulus

1. ## Solving inequality with modulus

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

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

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

2. 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:

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

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

3. but how would that change my answer?

4. 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.