Question

Solve for x: |x + 2| + 16 = 14

Answer 1

Okay, what do you think you should first do? :)

Answer 2

Subtract 16

Answer 3

this problem has no solution


subtract 16 from both sides of the equation and you get

\[\left| x + 2 \right| = -2\]

doesn't work

Answer 4

Yep, from both sides so:

14-16 = -2

Then what do you think you should do?

Answer 5

That's what I was thinking. It had no solution. And I would honestly check to see if it's right.

Answer 6

No wait, there is a solution.

Answer 7

How?

Answer 8

Subtract 2 from both sides.

-2 - 2 = -2 + (-2) = -4
And since it's the absolute value of i, then it would be positive 4.

i = 4

Answer 9

Does that make sense?

Answer 10

No not really... :/

Answer 11

Uhmmm....

l x + 2 l + 16 = 14
l x + 2 l + 16 - 16 = 14 -16
l x + 2 l = -2
l x + 2 - 2 l = -2 - 2
l x l = -4
x = 4

Answer 12

It's the absolute value of x, which makes the answer positive.

Answer 13

well I think @YoungStudier is attempting to use the identity that

\[i^2 = -1\]

it's used in complex numbers

so you would have

\[\left| x + 2 \right| = 2i^2\]

so then you get 2 solutions

\[x = -2 \pm 2i^2\]

but I'd expect that you are working with real numbers

Answer 14

Uhm..... No, well, I don't know, I'm just solving it the way K12 taught me to. :P

Answer 15

no, you are asked to find a value for x, that when added to 2 and the absolute value is taken, the asnwer is -2

it doesn't exist

Answer 16

well is someone taught you to solve it in that fashion, I'd suggest you ask to change classes...

Answer 17

@Yungwisdom2000 , are you doing K12?

Answer 18

and when you solve an absolution value equation such as

\[\left| x - 5 \right| = 10\]

there are 2equations to solve

1. x - 5 = 10 and 2. x - 5 = -10

both solutions are valid.

Answer 19

K12?? No. And I'm lost right about now