Question

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

Answer 1

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

Answer 2

Answer:

The solution of the given inequality  $|x-4|$ is $1$

Step-by-step explanation:

Given inequality $|x-4|$

We have to find the solution of the given inequality  $|x-4|$

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

$-3$

Rewrite as $x-4$

Consider , $x-4>-3$

Adding 4 both side, we have,

$x-4+4>-3+4$

Simplify, we have,

$x>1$

Consider , $x-4$

Adding 4 both side, we have,

$x-4+4$

Simplify, we have,

$x$

Combining, we have,

$1$

Thus, The solution of the given inequality  $|x-4|$ is $1$