# Thread: Absolute Value equation

1. ## Absolute Value equation

3 Ix+3I = Ix-3I+2x

I used the letter (I) and the line for the absolute value. Thanks for your help.

2. Originally Posted by MathMack
3 Ix+3I = Ix-3I+2x

I used the letter (I) and the line for the absolute value. Thanks for your help.
By the way, your keyboard has a key | that is just above the "enter" key. Use that for absolute value.

$3|x + 3| = |x - 3| + 2x$

There are 3 intervals you need to consider: $(-\infty, -3),~(-3, 3),~(3, \infty)$

On $(-\infty, -3)$ the equation reads
$3(-x - 3) = -(x - 3) + 2x$

On $(-3, 3)$ the equation reads
$3(x + 3) = -(x - 3) + 2x$

On $(3, \infty)$ the equation reads
$3(x + 3) = (x - 3) + 2x$

One, or more, of these equations will give you your solution set.

-Dan

3. I'm a little confused, so if I do one of them equations it will give me the answer or what I need for the problem?

4. Originally Posted by MathMack
I'm a little confused, so if I do one of them equations it will give me the answer or what I need for the problem?
You need to do all three to see which one will give you a solution. For example, the first two give the same solution, which are both inside (barely) their regions of applicability. The third equation has no solution.

-Dan