Solve for x: −4|x + 5| = −16

Question

torialaw192 · Answer

Okay, what do you get if you subtract 5 from both sides?

jim_thompson5910 · Answer

You have to divide both sides by -4 first

legomyego180 · Answer

yup

radar · Answer

Is this a complex numbers problem?  is the I actually i (for imaginary)

legomyego180 · Answer

how could it be complex? there is no radical

legomyego180 · Answer

Oh I see, no its an absolute value problem, @radar

legomyego180 · Answer

Since nobody else is explaining it ill have a go

$$|x+5|=4$$

Recall, numbers inside of the absolute value always have to be positive, this is the fact that will allow us to solve this problem.

The obvious answer is:

x= -1 here right?

Plug in -1 for x you get |-1+5| = 4 which satisfies the equation.

The not so obvious thing we need to realize is that |-4| = 4

So in addition to solving for 4 we also need to solve for -4.

|-9+5| = |-4| = 4

So x =-1, x =-9

jim_thompson5910 · Answer

Another method is to break up |x+5| = 4 into the two equations

x+5 = 4
x+5 = -4

then solving each for x. You'll get the same two answers. The rule I'm using is

`if |x| = k then x = k or x = -k where k is some positive number`

eg: if |x| = 5, then x = 5 or x = -5

radar · Answer

Sorry if brought confusion to the problem.  I mistook the I for a capital i, and overlooked that it was an absolute value problem.

mathmale · Answer

@kdvldhvlaid:  Hope this input has been helpful.  Please at least acknowledge others' efforts to help you, and please close your post when you're satisfied with your result.  Thank you.