Question

What is the solution to the inequality |x-4|<3

Answer 1

The solution of the given inequality
`|x-4|<\:3\:` is
`1<x<7`

Explanation:

Given inequality
`|x-4|<\:3\:`

We have to find the solution of the given inequality
`|x-4|<\:3\:`

Using absolute rule,
`\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a`, we have,

`-3<x-4<3`

Rewrite as
`x-4<-3\quad \mathrm{and}\quad \:x-4<3`

Consider ,
`x-4>-3`

Adding 4 both side, we have,

`x-4+4>-3+4`

Simplify, we have,

`x>1`

Consider ,
`x-4<3`

Adding 4 both side, we have,

`x-4+4<3+4`

Simplify, we have,

`x<7`

Combining, we have,

`1<x<7`

Thus, The solution of the given inequality
`|x-4|<\:3\:` is
`1<x<7`

Answer 2

Unfold it and add 4.
-3 < x-4 < 3
1 < x < 7