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- anonymous

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

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- anonymous

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

- chestercat

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- anonymous

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

- anonymous

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

- anonymous

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

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- mathstudent55

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

- LynFran

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

- mathstudent55

\(\large |x| - 8 = -~5\)
\(\large ~~~~~+8~~~~~+8\)

- anonymous

so 16 and 3?

- mathstudent55

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

- mathstudent55

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

- anonymous

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

- LynFran

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

- mathstudent55

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

Do you understand now how we add 8 to both sides to isolate \(|x|\)?

- anonymous

yea

- anonymous

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

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

- mathstudent55

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

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

- mathstudent55

With your problem, the equation now is
\(\large |x| = 3\)
We separate it into two equations:
\(\large x = 3\) or \(\large x = -3\)
Since these two equations are already solved for x, that is the final solution.

- LynFran

yep ^^

- mathstudent55

Let's go back to the -8 part above that is still bothering you.
Subtraction is defined as adding the opposite.
8 - 2 means 8 + (-2)
-3 - 4 means -3 + (-4)
5 - (-7) means 5 + 7
In general, for numbers a and b,
a - b means a + (-b)
That is simply the definition of subtraction.
In our equation, we are subtracting 8 from the absolute value of x.
We can turn the subtraction of 8 into the addition of the opposite of 8.
The opposite of 8 is -8, so
\(\large |x| - 8 = |x| + (-8) \)
Then when we add 8 to both sides to eliminate the -8 on the left side,
we end up with -8 + 8 which zero. That is how we eliminate the -8
from the left side and end up with only \(\large |x|\) on the left side.

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