## anonymous one year ago What is the solution of |-1+x| = 5 ?

1. anonymous

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

2. anonymous

@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

3. geerky42

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

4. anonymous

yeah, like @geerky42 said ;)

5. anonymous

@geerky42 where do you get negative 5 from?

6. geerky42

absolute value of -5 is 5. So one of possible values of $$x-1$$ is -5.

7. anonymous

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

8. geerky42

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 $$|\text-5| = 5$$

9. geerky42

Absolute value make all negative number positive, right?

10. geerky42

Also it does nothing to positive number or zero

11. anonymous

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

12. geerky42

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.

13. geerky42

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?

14. geerky42

Solve for x: $$x-1 = -5$$

15. anonymous

@geerky42 so that'd be -4 right

16. geerky42

Yeah. Now plug $$x=-4$$ into original equation; $|x-1| = 5$

17. geerky42

$|(-4)-1| = 5$

18. geerky42

Is equation true?

19. anonymous

@geerky42 it looks like it

20. geerky42

Does this clear up why we set $$x-1$$ equal to -5?

21. anonymous

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

22. geerky42

ok. you have one more equation $$x-1 = 5$$, but you can handle it. Welcome.