Question

Solve for x.

1+|2+x|=9

Answer 1

@zepdrix
@mathmale
plz help me

Answer 2

You could greatly simplify this problem if you'd please subtract 1 from both sides. Try to explain in your own words why you'd do that.

What's the next step? The resulting absolute value equation has 2 solutions. How would you go about finding them?

Answer 3

to separate the variable?

Answer 4

To simplify the equation, the whole equation.

You end up with |2+x|=8.

What next?

Answer 5

divide
2/2 and 8/2?

Answer 6

Why divide? There's no multiplication in |x+2|=8.

Answer 7

because thats what i usually do when solving for x

Answer 8

Unfortunately that's not good enough a reason.

What is the absolute value of -3?
What is the absolute value of 7?

Answer 9

3 and 7

Answer 10

Yes. The absolute value operator changes - numbers to + ones.

Thus, |x+2|=8 can be broken into 2 separate equations:

+(x+2)=8 and
-(x-2)=8

Can you solve the first equation for x?

Answer 11

4

Answer 12

show your work, please. Unfortunately, 4 is not the solution.

Simplify +(x+2)=8 now. Show your work and your result.

Answer 13

You may be confusing addition with multiplication.

Answer 14

2/2 8/2

Answer 15

No division either, Jamal. Why divide here?

+(x+2)=8 You can simply drop the first + sign and drop the parentheses ( ).

Please do that now.

Answer 16

10

Answer 17

Jamal, did you follow my instructions? You have +(x+2)=8. I asked you to OMIT (get rid of) the first + sign. Do that now, please.

Answer 18

x+2=8

Answer 19

much better. Thank you. Now solve that for x. Subtract 2 from both sides. Show your work.

Answer 20

2-2 = 0 8-2 = 6

Answer 21

6x

Answer 22

x = 6

Answer 23

x=6 is correct.

But your "2-2 = 0 8-2 = 6" while "right," is hard to follow / read.

I recommend you do it like this: x + 2 = 8
-2 = -2
------------

You end up with x = 6.

Answer 24

ok thanku

Answer 25

Now look at the other solution:

-(x+2)=8

Think: What do you have to do first? Goal: solve this equation for x.

Answer 26

You want to isolate (solve for) x.

Answer 27

drop the - and () make it x + 2 = 8

x + 2 = 8
-2 = -2

x = 6

Answer 28

Can't drop the -.

-(x+2)=8

Try multiplying both sides of this equation by (-1). Show your results.

Answer 29

x + -2 = -8

Answer 30

If you have -(x+2)=8 and mult. both sides by -1, you get

x+2=-8. Is this clear? If not, ask questions.

Answer 31

why is it not -2 if you multiply both sides

Answer 32

Because multiplying -(x+2) by -1 results in +(x+2).

Answer 33

You still have a neg. sign in the equation, but now it's in front of 8.