Question

Solve for x: |x − 2| + 10 = 12

x = 0 and x = 4

x = −4 and x = 0

x = −20 and x = 4

No solution

Answer 1

1) subtract 10 from both sides

Answer 2

The easiest way I've found to do these is to treat the absolute brackets as a plus/minus parenthesis.
So |x − 2| + 10 = 12
becomes:
+(x - 2) + 10 = 12
-(x - 2) + 10 = 12
From here just solve each equation separately.

Answer 3

The reason why the above may not work in every case is that there may be extraneous solutions.

It's a matter of chance that it worked here.

Answer 4

Im so confused :'(. And I'm going to fail because I don't unerstand

Answer 5

Is it No Solution?

Answer 6

There is a solution set. @ParthKohli is correct but you can simply plug each answer back into the original equation to check for the extraneous solution(s). What exactly are you having trouble with understanding?

Answer 7

I'm lost on the sets.I just got -20 and 4

Answer 8

On these two sets?
+(x - 2) + 10 = 12
-(x - 2) + 10 = 12

Answer 9

yes.

Answer 10

what did you get

Answer 11

Well for the first one:
+(x - 2) + 10 = 12
+(x - 2) = 12 - 10
x = 12 - 10 + 2
`x = 4`
Second:
-(x - 2) + 10 = 12
-(x - 2) = 12 - 10
2 - x = 2
`x = 0`

Answer 12

So A. I get it now :)

Answer 13

Solve for x: −4|x + 5| = −16

x = 21 over 4, x = −11 over 4

x = −1, x = 9

x = −1, x = −9

No solution

Answer 14

This is my last one

Answer 15

Okay but just be aware this won't always work as sometimes there are extraneous solutions as mentioned before. Go ahead and see if you can figure it out, then plug the two values you get back into the original equation to see if it's true.

Answer 16

I got No solution I plugged them in and both were negative

Answer 17

Go through the process with me on here and I'll see whats might be going on. There are solutions to this one as well.

Answer 18

Its either x = −1, x = −9 or x = 21 over 4, x = −11 over 4

Answer 19

And Im feeling the -9 and -1 but two solutions negative would result into no solution. that said we have to go to the 21 over 4 and -11 over 4

Answer 20

Okay so the original equation is: −4|x + 5| = −16
Lets get the abs by itself by dividing over the -4: |x + 5| = 4
Now breaking it up into a plus/minus parenthesis:
+(x + 5) = 4
-(x + 5) = 4
Do you understand this so far?

Answer 21

Yes

Answer 22

For the first one: +(x + 5) = 4
x = 4 - 5
`x = -1`
Second: -(x + 5) = 4
x + 5 = -4
x = -4 - 5
`x = -9`
Substitute both of these back into the original:
\(\bf { For: x = -1 }\)
−4|(-1) + 5| = −16
-4|4| = -16
-16 = -16 TRUE
\(\bf {For: x = -9 }\)
−4|(-9) + 5| = −16
-4|-4| = -16
-16 = -16 TRUE

Answer 23

So which one is it?

Answer 24

Since after plugging them into the original equation, they were both true statements, this means they are both solutions. If one was not true, this one is the extraneous. If both are not true there is probably no real solution. To this one, the answer is `x = -1 and x = -9`

Answer 25

thank you

Answer 26

You're welcome, good luck on your test!

Answer 27

Thank you, I need all the luck I can get ;)