value of x lies in number line as [tex]1<x\leq 10[/tex] and [tex]-10\leq x<-1[/tex] .
Step-by-step explanation:
Here , we need to tell where on a number line the value of x is for expression [tex]|x|>1[/tex] . Let's find out:
We know that for a Modulus function the value inside modulus is both positive & negative depending on value of x , So
x is positive :
Equation will be
⇒ [tex]x>1[/tex] , That means all numbers which are greater than 1 are included i.e. from 1 to 10 , where 1 is not included as x is strictly greater than 1 .
x is negative :
Equation will be
⇒ [tex]-x>1[/tex]
⇒ [tex]-x(-1)>1(-1)[/tex]
⇒ [tex]x<-1[/tex] , That means all numbers which are less than -1 are included i.e. from -1 to -10 , where -1 is not included as x is strictly less than -1 .
Therefore , value of x lies in number line as [tex]1<x\leq 10[/tex] and [tex]-10\leq x<-1[/tex] .
