Question

What is the solution of |-1+x| = 5 ?

Answer 1

In absolute value equation
-1+x=5
And
-1+x=-5
What are the two possible values of x?

Answer 2

@gaos in absolute value wouldn't it just be 1+x=5 I'm a little lost I thought absolute value made whatever's in the brackets positive

Answer 3

Yeah, so that mean there is two possible values for x-1; -5 OR 5

Since |5| = 5 AND |-5| = 5

Answer 4

yeah, like @geerky42 said ;)

Answer 5

@geerky42 where do you get negative 5 from?

Answer 6

absolute value of -5 is 5.

So one of possible values of \(x-1\) is -5.

Answer 7

@geerky42 but the 5 isn't in the brackets i'm sorry i'm just confused

Answer 8

Here, we have \[\Large |x-1| = 5\]

So value of \(x-1\) itself could be either 5 OR -5. we don't know which.

So we split it into two cases:

\(x-1 = 5\)
OR
\(x-1 = \text-5\)

Because \(|5| = 5\) and \(|\text-5| = 5\)

Answer 9

Absolute value make all negative number positive, right?

Answer 10

Also it does nothing to positive number or zero

Answer 11

@geerky42 i completely understand that part i just don't understand how it could be -5 when it says it equals 5

Answer 12

One of case is \(x-1 = -5\)

Because when you replace \(x-1\) to \(\text-5\) in absolute value (in original equation), then you would have \(|\text-5|\), which is equal to 5.

Answer 13

Ok how about this? You just go ahead and solve for x in \(x-1 = -5\)

Then you plug whether x equals to into original equation and see if it is true?

Answer 14

Solve for x:

\(x-1 = -5\)

Answer 15

@geerky42 so that'd be -4 right

Answer 16

Yeah. Now plug \(x=-4\) into original equation;
\[|x-1| = 5\]

Answer 17

\[|(-4)-1| = 5\]

Answer 18

Is equation true?

Answer 19

@geerky42 it looks like it

Answer 20

Does this clear up why we set \(x-1\) equal to -5?

Answer 21

@geerky42 yes it does thank you so much for all the help!

Answer 22

ok. you have one more equation \(x-1 = 5\), but you can handle it.

Welcome.