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

Question

asked Oct 26, 2018 133k views

2 Answers

Ruffen · Answer 1 · 2018-10-29T09:15:14+0000

Answer:

The solution of the given inequality
$|x-4|<\:3\:$ is

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