Question

RSM HW HELP!!! PLEASE SOLVE A.S.A.P!

Answer 1

value of x lies in number line as
`1<x\leq 10` and
`-10\leq x<-1` .

Explanation:

Here , we need to tell where on a number line the value of x is for expression
`|x|>1` . 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

⇒
`x>1` , 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

⇒
`-x>1`

⇒
`-x(-1)>1(-1)`

⇒
`x<-1` , 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
`1<x\leq 10` and
`-10\leq x<-1` .