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

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Answer 1 · 2015-08-08T01:11:21

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

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

$| a - b | < c$ $| a - b | < c$

becomes

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

So, you have

$| x - 3 | < 4$ $| x - 3 | < 4$

can be split up into

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

Now we can solve each inequality to get

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

$x - cancel(3) + cancel(3) < 4 + 3$

$x<7$

and

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

$x - cancel(3) + cancel(3) > -4 + 3$

$x>-1$

so your answer would be

$x > - 1$
$x < 7$

or

$-1 < x < 7$

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