Answer to Question #152713 in Algebra for O.Weerasinghe

Question

2x - 1 < x*x - 4 < 12
solve with steps

Answer 1

$$\begin{alignedat}{2} x^2-4>2x-1 \\ x^2-4 <12 \end{alignedat}$$

$$\begin{alignedat}{2} x^2-2x-3>0 \\ x^2-16 <0 \end{alignedat}$$

$$\begin{alignedat}{2} (x+1)(x-3)>0 \\ (x+4)(x-4) <0 \end{alignedat}$$

$$\begin{alignedat}{2} x<-1\ or\ x>3 \\ -4<x<4 \end{alignedat}$$

$$x\in(-4,-1)\cup(3,4)$$