Question

Okay so im trying to learn absolute values and such and I need help trying to figure out how to do this. The lesson itself is very difficult to understand, can anyone walk me through it?

Answer 1

what is the solution set of \left| x-6 \right|=4?\]

Answer 2

Ix-6I=4 there that looks better sorry

Answer 3

10

10 or -10

-2 or -10

2 or 10
These are some answers but dont give the answer please walk me through how to do it

Answer 4

@TheSmartOne Please help if you can

Answer 5

We would simplify the equation....since it is in absolute the total can be of positive or negative so we have two equations...

\(\huge{x-6=4}\)

\(\huge{x-6=-4}\)

So we would simplify each equation to find the answer to x....

Answer 6

Thank you-- hold on let me write this down. Thank you give me one minute to write

Answer 7

np :)

Answer 8

So so with x-6=4 +6 x=10 and x-6=-4 +6 x=2 ?

Answer 9

Correct :)

Answer 10

Okay thank you so so much!

Answer 11

You very welcome ^^

Answer 12

Hah... okay quick question @563blackghost Would it be the same for equations that have numbers outside the lines? like Ix-4I+7=4? Would I do -7 from the equation or would I do -4+7 to combine like terms then subtract or add to the -4/4

Answer 13

With equations like that we would need to get the absolute to itself first....

\(\huge{|x-4|+7=4}\)

We would need to subtract 7 from each side...

\(\huge{|x-4|(7-7)=4-7 \rightarrow \color{red}{|x-4|=-3}}\)

Now you would apply what I had told you before :)

Answer 14

--Thank you let me write this down-- Sorry slow with writing

Answer 15

All's good :) and your welcome ^.^

Answer 16

So at that point it would be x-4=-3 and x-4=3?

Answer 17

Yup :)

Answer 18

so with that it would be x=7 and x=1 ??

Answer 19

Thank you so much again, sorry if I bug ya again though. Means a lot to not just have the answer blerted out. It helps much more to be walked through it. Thank you again.

Answer 20

` Absolute value is NEVER equal to a negative value.` So it would not have a solution....

And your welcome :)

If your confused on why it has no solution look at this link :)
http://www.regentsprep.org/regents/math/algtrig/ate1/abslesson.htm

Answer 21

Okay I think I understand the negative parts of it and I see and understand if there is a longer equation on both sides, but say I2x+4I<10 with this I did what you had shown me. I got 2x+4=10 thinking this is correct then go back and add in the x.

2x+4=10 2x+4=-10

x=3 and x=-7

Since the original equation is I2x+4I<10

do I set up the equations like I2(3)+4I<10 and I2(7)+4I<10?

Answer 22

@563blackghost

Answer 23

Do not change the sign of the problem it stays as `<`. The total will only change so you have two equations...

\(\huge{2x+4<10}\)

\(\huge{2x+4<-10}\)