Question

Solve.
|3 – 2x| = 9
A.
x = –3
B.
x = 6
C.
x = –3, x = 6
D.
x = 3, x = 6

Answer 1

The absolute bars are telling us that there will be two solutions.\[\Large\rm |3 – 2x| = 9\]\[\Large\rm \pm(3 – 2x) = 9\]Rewrite the plus/minus on the other side, makes things easier to work with.

Answer 2

\[\Large\rm 3 – 2x = \pm9\]

Answer 3

Do you understand how to find your two solutions from this point?

Answer 4

no:(

Answer 5

So I guess we could start by subtracting 3 from each side, yes?

Answer 6

\[\Large\rm -2x=\pm9-3\]

Answer 7

Then to finish isolating the x we would divide both sides by -2,\[\Large\rm x=-\frac{1}{2}(\pm9-3)\]

Answer 8

To find the first solution, let the 9 be positive, and simplify it down to a number.
Then for your other solution, let the 9 be negative.

Answer 9

I still don't really understand it though I mean i kinda do and kinda dont at the same time :/

Answer 10

wait so are you saying add 9 to both side? because i'm not sure

Answer 11

Ok let's try a different approach.
I think maybe the plus/minus symbol is confusing you.\[\Large\rm |3-2x|=9\]We can drop the absolute bars by writing this as:\[\Large\rm 3-2x=9\]\[\Large\rm 3-2x=-9\]These two equations represent the absolute function.
(They would normally be restricted to certain intervals of x, but we don't need to worry about that here).

Answer 12

Do you know how to solve for x in this equation?\[\Large\rm 3-2x=9\]

Answer 13

Or still confusing?

Answer 14

yea I can do that

Answer 15

That will give you your `first` solution.

Answer 16

Solving the other equation for x,\[\Large\rm 3-2x=-9\]will give you your `second` solution.

Answer 17

wait you add two to both sides right?

Answer 18

No no no.
Let's write it like this a sec,\[\Large\rm -2x+3=9\]3 is being `added` to each side, yes?
So we do the inverse, `subtract` 3 from each side.

-2 is `multiplying` the x, yes?
so we do the inverse, `divide` both side by -2.

Answer 19

ohhhhhhhhhhhhh ok thanks I think that I could do it now well atleast I think LOL but thx :)

Answer 20

hehe