Modulus function (Algebraic method)

Solve $\displaystyle |\frac{1}{a}|<1$, $\displaystyle a$ is a non-zero constant.

I solved this using graphical method and the answer is $\displaystyle a>1$ or $\displaystyle a<-1$ but I tried using the algebraic method and didn't got the same answer!

$\displaystyle |\frac{1}{a}|<1$

$\displaystyle -1<\frac{1}{a}<1$

$\displaystyle -1<a<1 $

What is wrong with my workings?

Re: Modulus function (Algebraic method)

Quote:

Originally Posted by

**Punch** Solve $\displaystyle |\frac{1}{a}|<1$, $\displaystyle a$ is a non-zero constant.

I solved this using graphical method and the answer is $\displaystyle a>1$ or $\displaystyle a<-1$ but I tried using the algebraic method and didn't got the same answer!

$\displaystyle |\frac{1}{a}|<1$

$\displaystyle -1<\frac{1}{a}<1$

$\displaystyle -1<a<1 $

What is wrong with my workings?

$\displaystyle \left|\frac{1}{a}\right|< 1 \Rightarrow \frac{|1|}{|a|} < 1 \Rightarrow |1|<|a| \Rightarrow |a| > 1$