# How do you solve abs(x-3)<4?

Aug 8, 2015

$- 1 < x < 7$

#### Explanation:

Absolute value functions can be split up into two functions; represented in variable form, it would look like

$| a - b | < c$

becomes

$a - b < c$ and $a - b > - c$

So, you have

$| x - 3 | < 4$

can be split up into

$x - 3 < 4$ and $x - 3 > - 4$

Now we can solve each inequality to get

$x - 3 < 4$ $\to$ add 3 to both sides

$x - \cancel{3} + \cancel{3} < 4 + 3$

$x < 7$

and

$x - 3 > - 4$ $\to$ add 3 to both sides to get

$x - \cancel{3} + \cancel{3} > - 4 + 3$

$x \succ 1$

$x > - 1$
$x < 7$
$- 1 < x < 7$