Question

Graphically solve this:
|2x-2|=9
I forgot how to do this... help?

Answer 1

Can I start with taking the absolute lines off and making the -2 a positive? like 2x+2=9 ?

Answer 2

Whenever you see |A| = B, then you have to solve two equations without the absolute bars: A = B and A = -B

Answer 3

okay now it would be 2x+2=9 because its positive ?
2x=7
x=3.5
?

Answer 4

Not 2x+2. 2x - 2.

Answer 5

are we just assuming its off and then we do calculations and then we put the absolute bars back on?

Answer 6

at the

Answer 7

end

Answer 8

2x-2=9
2x=11
x=5.5?

Answer 9

|2x-2|=9
If 2x-2 is positive, the absolute bar does do anything because it is already positive.
So for the case 2x-2 > 0: 2x - 2 = 9, 2x = 11, x = 5.5

If 2x-2 is negative, the absolute bar changes it to -(2x-2) and makes it positive. So -(2x-2) = 9 or 2x - 2 = -9; 2x = -7; x = -3.5

So the two solutions are: x = -3.5 and x = 5.5

Try putting each of the value back into the equation and you will see they are true.

Answer 10

If 2x-2 is positive, the absolute bar does NOT do anything because it is already positive.

Answer 11

i thought it changed everything things inside the bars, but i see i guess, so if it was |-2x+2| it would be 2x+2?

Answer 12

but if it was already |+9999x+9999| it'd stay the same

Answer 13

wthiuout bars

Answer 14

9999x+9999

Answer 15

No. You have to look at the whole thing and not the sign on individual things.
|-2x+2| does not change to 2x+2.

You have to consider two cases. If the value of the variable x is such that -2x+2 is positive, then the absolute bars can be dropped because -2x+2 is already positive. The next case is if the value of the variable x is such that -2x+2 is negative, then the absolute bars will change it to -(-2x+2) to make it positive and now the absolute bars can be dropped.

The simplest way to remember is: If |A| = B it implies A = B and -A = B or A = -B.

Answer 16

Oh to find the X's you have to do the 'two case "assuming" method'. I think thats what I was forgetting. Maybe.

Answer 17

But this is how I remember it. If you have one equation that has absolute bars you have to solve two equations: |A| = B implies A = B and A = -B

|2x-2|=9 implies 2x - 2 = 9 or 2x - 2 = -9
2x = 11 or 2x = -7
x = 5.5 or x = -3.5

Answer 18

ok I SEe!

Answer 19

WILL THIS WORK ALL THE TIME?

Answer 20

Yes.

Answer 21

OKAY I did them and i got the same answers as yours, -3.5 and 5.5

Answer 22

so (-3.5,9) and (5.5,9)

Answer 23

And you can verify they are true by plugging them back into the original equation:

put x = -3.5 in |2x-2|. |2*(-3.5) - 2| = |-7 - 2| = |-9| = 9 (true)
put x = 5.5 in |2x-2|. |2*(5.5) - 2| = |11 - 2| = |9| = 9 (true)

Answer 24

yes i did that, :D

Answer 25

The answer is simply x = -3.5 and x = 5.5
This is an equation with no y-values involved and so don't put them in ordered pair (x,y).

Answer 26

im supposed to graph it

Answer 27

i think teacher ment doing the V thing

Answer 28

cause we did do one of those in class. we are revising for pre calc 30

Answer 29

we are revising pre calc 20

Answer 30

To solve the equation graphically do the following:
|2x-2| = 9
|2x - 2| - 9 = 0

Plot y = |2x - 2| - 9. The points where it crosses the x-axis will have y = 0 and those are the solutions.

Answer 31

the two solutions are on a number line (the x-axis)

Answer 32

sorry laptop died

Answer 33

if x is 1 y is -9?

Answer 34

y = |2x - 2| - 9
put x = 0; y = |0 - 2| - 9 = 2 - 9 = -7. So (0, -7)
put x = 1; y = |2 - 2| - 9 = 0 - 9 = -9 So (1, -9)

Answer 35

it seems odd compared to you graph

Answer 36

Mine is a rough sketch not to scale and not done on a graph paper.

Answer 37

okay. then I get it!

Answer 38

I have more of these, do you have time? (complicated ones)

Answer 39

http://prntscr.com/4jiovf

Answer 40

o wow! i see

Answer 41

Close this question and post it separately. I have to log off now but others may help.

Answer 42

I was look at wolfram alpha graph it didnt look the same http://www.wolframalpha.com/input/?i=%7C2x-2%7C%3D9

Answer 43

http://www.wolframalpha.com/input/?i=y+%3D+ |2x-2|-9

Answer 44

Look at the second graph in the above Wolfram link.

Answer 45

this one? http://www.wolframalpha.com/input/?i=abs%282%20x-2%29-9%20%3E%200&lk=2

Answer 46

why greater than 0. You are not solving am inequality here but an equation.

Answer 47

now I'm wasting both our times. Well I guess good night thanks for helping me!!!!

Answer 48

you are welcome.

http://www.wolframalpha.com/input/?i=abs%282+x-2%29-9+%3D+0