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In absolute value equation -1+x=5 And -1+x=-5 What are the two possible values of x?
@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
Yeah, so that mean there is two possible values for x-1; -5 OR 5 Since |5| = 5 AND |-5| = 5
yeah, like @geerky42 said ;)
@geerky42 where do you get negative 5 from?
absolute value of -5 is 5. So one of possible values of \(x-1\) is -5.
@geerky42 but the 5 isn't in the brackets i'm sorry i'm just confused
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 \(|\text-5| = 5\)
Absolute value make all negative number positive, right?
Also it does nothing to positive number or zero
@geerky42 i completely understand that part i just don't understand how it could be -5 when it says it equals 5
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.
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?
Solve for x: \(x-1 = -5\)
@geerky42 so that'd be -4 right
Yeah. Now plug \(x=-4\) into original equation; \[|x-1| = 5\]
\[|(-4)-1| = 5\]
Is equation true?
@geerky42 it looks like it
Does this clear up why we set \(x-1\) equal to -5?
@geerky42 yes it does thank you so much for all the help!
ok. you have one more equation \(x-1 = 5\), but you can handle it. Welcome.