Question

Solve the absolute value equation or indicate that the equation has no solution.

│x + 6│ = 9

A. {3}

B. {-15, 3}

C. {-3, 15}

D. ø

Answer 1

@Mertsj

Answer 2

its either B or D

Answer 3

Well, either 9 or -9 inside there is = to 9 after the abs val.

Answer 4

but the solution is 3,-15

Answer 5

So, solve for both of those.

Answer 6

Yes. because of both of those.

\(x+6=9\)
\(x+6=-9\)

That is what the absolute value means.

Answer 7

so B is the correct option

Answer 8

Yes, absolutley!

Answer 9

Do you get how I chose those equations to solve? That is the key here.

Answer 10

Can you tell me this key

Answer 11

Sure!
\[|-9|=9\\|9|=9\]Right?

Answer 12

|21| is we write it without the absolute it will be 21 right

Answer 13

And same with -21.

Answer 14

Yes, of the right hand side is any negative, there is no way what is inside the ABS can be negative.

Answer 15

http://prntscr.com/15fm64

for example this question

Answer 16

will it be C or D

Answer 17

But back to the -9 and 9 for a moment. Because what was inside the absolute value could have been either -9 or 9, I have to set it to both and solve each.

As for the cube root problem, cubes play by different rules.

Answer 18

http://prntscr.com/15fm64

iam talking about this one

Answer 19

Yes, I know. You asked for the key.... then moved on. I just wanted to finish the key in case you really did want to learn it.

For the cubic root or any odd power, what happens with the negative?

Answer 20

Powers and roots are related. The even odd rules for them are also related.

The rules for the sign of \((-1)^2\) and \((-1)^3\) translate to rules about roots. With the even roots, like \(\sqrt{-1}\) and \(\sqrt[4]{-1}\), there is no way to get a real answer out. But what about odd ones?