Question

How do I transform an absolute value equation into two linear equations? One of the problems is:

Transform the absolute value equations into two linear equations. Then Solve |x-10|=17

I know what I would do if i just had to find x, but how do change it into 2 linear equations?

Answer 1

sorry my notifications aren't working
what did you get for x for the other equation you were working?

Answer 2

like both x's

Answer 3

for the other one I got that the extraneous solution was x=-2

and for this one like do I just write x= the two xs as the entire equation?

Answer 4

right but did you find the solution that was actually a solution for the other equation?

Answer 5

also again|x-10| can be written as (x-10) or -(x-10)
so just like the other you will have two equations

Answer 6

x-10=17 or -(x-10)=17

Answer 7

whenever you have |f(x)|
just say okay well that could either be f(x) or -(f(x))

Answer 8

For the first one, the solution that was actually a solution would be 6=x, the other one?

and for the second one, would the two linear equations be x-10=17 and -(x+10)=17 or do I need to solve and then use the 2 x answers as the linear equation?

Answer 9

ok good on the first one
x=6 was a solution
x=-2 was an extraneous solution
it says to write as two separate linear equations which we did. And then it says solve.
so you need then solve x-10=17 and solve also -(x+10)=17

Answer 10

so you have x-10=17 and x+10=-17 to solve

Answer 11

what do you get as solutions?

Answer 12

I got x=27 and x=-7
I'm just confused about the whole linear equation thing

Answer 13

well x-10=17 and -(x+10)=17 are both linear equations (these equations aren't simplified)
x=27 and x=-7 are both linear equations too (these linear equations are simplified)

Answer 14

wow and i wrote that one equation wrong twice
-(x-10)=17*

Answer 15

x-10=-17
x=-17+10=-7 which is what you got

Answer 16

So the answer is just x=27 and x=-7?

Answer 17

is this like where you enter into a computer software thing?
or is this written work you turn into your teacher?

Answer 18

x=27 or x=-7 or the solutions and also linear equations

Answer 19

It is written work. Why? I have a test coming up and I just want to make sure I'm understanding everything

Answer 20

if it is written work i think you to say well |x-10|=17 can be transformed into the two linear equations x-10=17 or x-10=-17.
And then for the solving part you would x=27 or x=-7.

Answer 21

Okay thanks!

Answer 22

np