Question

Solve for x: |x| − 8 = −5

x = −13 and x = −3

x = 3 and x = −3

x = 3 and x = 13

No solution

Answer 1

|x| - 8 = -5
Add 8 to both sides.
-5 + 8 = 3
x=3

Since we know that the absolute value bars also mean the same thing as the distance from the number to 0, the absolute value of a number is always positive. We can say |-3| becuase that will equal to positive 3 (which is x).

Your answer can be both |-3| and/or |3|.

Answer 2

So B?

Answer 3

Yes

Answer 4

ok Thank you can u help with a few more?

Answer 5

Sure

Answer 6

I'd be more comfortable (a lot more) NOT using those absolute value symbols in stating your solutions. I'd write "the solutions are 3 and -3."

Answer 7

Solve for x: -3|x + 7| = -12

x = 5 over 3, x = −19 over 3

x = −3, x = −11

x = −3, x = 11

No solution

Answer 8

The original equation is true if you substitute either -3 or 3 for x.

Answer 9

ok.

Answer 10

Do you know how to solve for x in an equation becuase all of these equations are really the same concept?

Answer 11

Wouldnt you distribute the -3?

Answer 12

Yes towards x and 7.

Answer 13

so -3x + -21

Answer 14

Yes

Answer 15

So then would i add 12?

Answer 16

Then you can solve for x from there becuase you know the solution is -12.

Answer 17

Shade: Here's an alternative approach:
Divide the original equation by -3. Then we have the simpler |x+7| = 4.
Please verify that the two solutions to this are -3 and -11.

Answer 18

I got that so its right -3 and -11?

Answer 19

No. Since you want to isolate the variable to get the original amount. To do that, you want to take out any integer that there are before or after it to only have the coefficient by itself. That means that you have to instead subtract (the inverse of addition) -21 to 12. Using that sum you can then divide by 3 (since multiplication is the inverse of division).

Answer 20

|x| − 8 = −5
+ 8 + 8
|x| = 3
^ That would be one solution -

Answer 21

(1) What do you propose is the correct response to this question?
(2) Are -3 and -11 solutions to the original absolute value problem?
(3) Are -3 and -11 solutions to the simplified absolute value problem |x+7| = 4?

Answer 22

Oh wait - Wrong problem LOL

Answer 23

Shade, yes, I believe -3 and -11 are the solutions we were looking for. Unforunately, calculusxy disagrees. See my questions (2) and (3) (above). Best wishes to you.

Answer 24

So what is the correct answer yall have me soo confused

Answer 25

OK so i have one more i need to ask

Answer 26

Solve for x: |2x + 6| − 4 = 20

x = 9 and x = 11

x = −9 and x = 15

x = 9 and x = −15

No solution

I believe the answer is no solution! Please tell me if i am incorrect

Answer 27

Would be x = -11 and x = -3 ---> http://www.wolframalpha.com/input/?i=+x%3A+-3%7Cx+%2B+7%7C+%3D+-12+solutions+ <--- As @mathmale Said :)

Answer 28

@mathmale I answered ShadePorter's question of "So then would I add -12?"

Answer 29

Shade, please check the proposed solutions yourself. Substitute x = -3 into the original absolute value equation. Is the result true or false?
Substitute -11 and do the same. Is the result true or false?

Answer 30

@ShadePorter Looks like you made a mistake - There are two solutions there :)

Answer 31

Charlotte, thanks! Made my day.
Good night, all. I need my beauty sleep. Solve absolute value problems in your dreams.

Answer 32

Take out the absolute value bars, since the positive numbers are already positive. Then solve for x.

Answer 33

@mathmale Really?! HUZZAH! Glad to have made your day - You just made mines! xD Goodnight and take care!

Answer 34

please tell me if i am correct on the "no solution problem"

Answer 35

I believe that there is only one solution which is is supposed to be 9. I don't find any other solutions to this other than 9.

Answer 36

@ShadePorter Not correct I'm afraid. You can do it! Try solving it again :)

Answer 37

All i got was 9 as well but all the multiple choice answers also have 11 and i have only got 9? Im soo lost

Answer 38

Or 15

Answer 39

I'll go with no solutions becuase none of the options above make sense other than 9.

Answer 40

Thank you soo much!

Answer 41

No problem :) if you like my answer, you can be my fan :)

Answer 42

Thanks :) have a good night

Answer 43

Let's revisit Shade's second question.|
|2x+6| = 24
Dividing through by 2,
|x+3| = 12
Case 1: Assume x+3 is already positive. then x+3=12 and x = 9.
Case 2: Assume that x+3 is negative. Then the equation becomes -(x+3) = 12, or
x+3 = -12, or x=-15.
Verify both solutions by substituting them back into the original equation separately.