Solve for x: |x| − 8 = −5
Can someone explain the steps for how to solve this please?

Question

Solve for x: |x| − 8 = −5
Can someone explain the steps for how to solve this please?

anonymous · Answer

the answer is 3, but if you subtract 8-5 that equals 3 which will give you the answer

anonymous · Answer

its x - 8 = -5
the five is negative tho so..

anonymous · Answer

I just want to know the steps to figuring this out cuz i know thats not the right answer sorry..

mathstudent55 · Answer

First, add 8 to both sides.
Can you do that?

lynfran · Answer

$$|x|-8=-5$$ok 1st step it to add 8 to both sides of the equation

mathstudent55 · Answer

$\large |x| - 8 = -~5$
$\large ~~~~~+8~~~~~+8$

anonymous · Answer

so 16 and 3?

mathstudent55 · Answer

No. 
-8 + 8 = 0
-5 + 8 = 3. That is good.

mathstudent55 · Answer

You end up with 

$\large |x| = 3$

Ok so far?

anonymous · Answer

the 8 is not negative tho its x minus 8 equals negative 5

lynfran · Answer

example solve for x... $$|x|-7=9$$$$|x|=9+7$$$$|x|=16$$$$x=\pm 16$$

mathstudent55 · Answer

In our original equation, -8 (minus eight) means subtract 8.
A subtraction can always be written as the sum of the opposite.
So -8 means plus the opposite of 8.

$\large |x| - 8 = -5$

$\large |x| + (-~8) = -5$
$\large~~~~~~~~~~+8~~~~~+8$

After adding 8 to both sides, you get:

$\large |x| = 3$

mathstudent55 · Answer

Do you understand now how we add 8 to both sides to isolate $|x|$?

anonymous · Answer

yea

anonymous · Answer

the options for it tho aren't just one number its one of these

x = −13 and x = −3
x = 3 and x = −3
x = 3 and x = 13
No solution

anonymous · Answer

plus i dont understand how you turned minus eight into negative eight, i dont understand why you would do that cri

mathstudent55 · Answer

Ok. Now we have a simple absolute value equation.
On the left side we have just $|x|$. This equals a number, 3, on the right side.

Whenever you have an absolute value equation where something in absolute value signs equals a number, you separate it into two simple equations, both without absolute signs.

This is the pattern. Then I'll show you with your equation.

To solve the absolute value equation

$\large |x| = k$,    where k is a non-zero number,

solve these two equations

$\large x = k$   or   $\large x = -k$

lynfran · Answer

heres another example ... |dw:1439778127102:dw|