# Thread: Another absolute value problem

1. ## Another absolute value problem

How do yu find the AV of
|x - 5| = 8

2. Originally Posted by xxLOLAxx
How do yu find the AV of
|x - 5| = 8
Two cases:

Case 1:

$\displaystyle x-5=8$

Case 2:

$\displaystyle x-5=-8$

3. tHANKS. DO YU KNOW HOW TO FIND THE INEQUALITY OF
|x| 4

4. Originally Posted by xxLOLAxx
tHANKS. DO YU KNOW HOW TO FIND THE INEQUALITY OF
|x| 4
I'm not seeing your picture at all. Can you state the problem?

5. THE PROBLEM SAYS Solve the inequality. Graph the solution set.
|x| 4

6. Originally Posted by xxLOLAxx
THE PROBLEM SAYS Solve the inequality. Graph the solution set.
|x| 4
I see the | x | and the 4. I do not see the inequality symbol between them. You can use your keyboard for >, <, >=, <=.

Here are the general rules for absolute value inequalities:

If |a| > b, then a < -b or a > b.

If |a| < b, then -b < a < b.

7. WHAT ABOUT IN THIS PROBLEM
|x + 1| - 4 <= -1

8. Originally Posted by xxLOLAxx
WHAT ABOUT IN THIS PROBLEM
|x + 1| - 4 <= -1
$\displaystyle |x+1|-4 \leq -1$

First, you would add 4 to both sides. You need to isolate the absolute value part of your inequality.

$\displaystyle |x+1| \leq 3$

Now, use the rule from my last post that applies.

$\displaystyle -3 \leq x+1 \leq 3$

Subtract 1 from each part of the inequality.

$\displaystyle -3 \leq x+1 \leq 3$
$\displaystyle -1 \ \ \ \ \ \ -1 -1$
------------------------

$\displaystyle -4 \leq x \leq 2$

Solultion set= {$\displaystyle -4 \leq x \leq 2$} or [-4, 2]

9. WHAT IF THE PROBLEM IS LIKE THIS
|x - 5| = |8 - x|

10. Originally Posted by xxLOLAxx
WHAT IF THE PROBLEM IS LIKE THIS
|x - 5| = |8 - x|
Square both sides. Then solve for x.

$\displaystyle x^2-10x+25=64-16x+x^2$

11. THANK YU SO MUCH