Modulus function (Algebraic method)

**Punch** · December 6th 2011, 11:19 PM

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

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

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

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

$-1<a<1$

What is wrong with my workings?

**princeps** · December 7th 2011, 12:55 AM

Originally Posted by Punch

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

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

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

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

$-1<a<1$

What is wrong with my workings?

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

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