# |-2x|= |2x| why?

Discussion in 'Computer Support' started by Solar^, Dec 3, 2005.

1. ### Solar^Guest

Greetings Group,
Thought some of you programmer-mathematicians might be able to answer this
question - why doe |-2x| = |2x| and not just 2x? Studying for a math final
is why I want to know.
Regards,
Solar^

Solar^, Dec 3, 2005

2. ### JamesGuest

Because any double negatives multiplied together gives a positive answer.

if i recall my maths correctly:

negative multiplied or divided by a negative = positive
one negative multiplied or divided by a positive = negative

Ohh watch me get this one wrong James, Dec 3, 2005

3. ### philoGuest

because -2x does NOT = 2x

but the absolute value of -2x *does* equal the absolute value of 2x

if you have gotten to your finals...
you should know what "absolute value" means by now !

philo, Dec 3, 2005
4. ### Solar^Guest

Ok, Philo,
If x were 4, then |-2*4| = 8 -> 2*4 0r just plain 2x and |2x| seems a
little redundant since x is already a positive number. If it were a
negative number then |-2*-4| <> 2*-4 (2x) but rather |2x| ok.. got it
thanks!

Solar^, Dec 3, 2005
5. ### DCGuest

Not exactly.
This is true, but...

DC, Dec 3, 2005
6. ### FredGuest

If x is negative then 2x does not equal to |2x|.

Fred, Dec 3, 2005
7. ### Mike EasterGuest

I think it is useful to make a statement of the equation, or rather the
original question.

Why does the absolute value of -2x equal the absolute value of 2x, and
not just '2x'?

And, before we begin to answer the question, we remember something
important about absolute values and variables.

When you are dealing with a variable's value, you don't know the sign of
the value; that is, you don't know whether the variable x represents a
postive or negative value. So, if x is a negative value, the absolute
value of it changes the sign of the value, whereas if x is a positive
value, it doesn't.

Now back to our statement.

If x is a positive value, |-2x| = |2x| *AND* 2x *BUT*

If x is a negative value, [-2x| = |2x| *BUT NOT* 2x *because*

in the case of x being a negative value, 2x would also, which the
absolute values are not.

Mike Easter, Dec 3, 2005
8. ### Mike EasterGuest

Short form:

Because 2x can have a negative value, which the absolutes can't.

But, that answer doesn't seem to have a 'long enough' "why?" wrapped
around it.

Mike Easter, Dec 4, 2005
9. ### philoGuest

good!

BTW: it took me quite a few tries and many years to get anywhere in math!!!!

philo, Dec 4, 2005
10. ### john60Guest

I am not sure for the answer, this is what I remember:

|-2x| = |2x| is the same as |-a| = |a| ...and it's not an equation,
it's the definition of absolute value

No matter if x is negetive or positive, |-2x| = |2x|

Assume x = 4

|-2 * 4| = |2 * 4|
|-8| = |8|

since |8|=8 and |-8|=8|, then it indeed |-8| = |8|

Assume x = -3

|-2 * - 3| = | 2 * -3|
|6| = |-6|

since |6|=6 and |-6|=6, then indeed |-6| = |6|

Note that:

+ * + = +
+ * - = -
- * - = +

+ / + = +
+ / - = -
- / + = -
- / - = -

john60, Dec 4, 2005
11. Howdy!

Because X might be a negative number.

If x = -4, then -2x = 8, but 2x = -8.

But the absolute value of both are 8.

RwP

Ralph Wade Phillips, Dec 4, 2005
12. ### mdpGuest

Because the solution must be good for all x and for the case when x is
negative

|-2x| = |2x| does not equal 2x

mdp, Dec 4, 2005