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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    In absolute value equation -1+x=5 And -1+x=-5 What are the two possible values of x?

  2. anonymous
    • one year ago
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    @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
    • one year ago
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    Yeah, so that mean there is two possible values for x-1; -5 OR 5 Since |5| = 5 AND |-5| = 5

  4. anonymous
    • one year ago
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    yeah, like @geerky42 said ;)

  5. anonymous
    • one year ago
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    @geerky42 where do you get negative 5 from?

  6. geerky42
    • one year ago
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    absolute value of -5 is 5. So one of possible values of \(x-1\) is -5.

  7. anonymous
    • one year ago
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    @geerky42 but the 5 isn't in the brackets i'm sorry i'm just confused

  8. geerky42
    • one year ago
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    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
    • one year ago
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    Absolute value make all negative number positive, right?

  10. geerky42
    • one year ago
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    Also it does nothing to positive number or zero

  11. anonymous
    • one year ago
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    @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 year ago
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    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
    • one year ago
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    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
    • one year ago
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    Solve for x: \(x-1 = -5\)

  15. anonymous
    • one year ago
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    @geerky42 so that'd be -4 right

  16. geerky42
    • one year ago
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    Yeah. Now plug \(x=-4\) into original equation; \[|x-1| = 5\]

  17. geerky42
    • one year ago
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    \[|(-4)-1| = 5\]

  18. geerky42
    • one year ago
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    Is equation true?

  19. anonymous
    • one year ago
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    @geerky42 it looks like it

  20. geerky42
    • one year ago
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    Does this clear up why we set \(x-1\) equal to -5?

  21. anonymous
    • one year ago
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    @geerky42 yes it does thank you so much for all the help!

  22. geerky42
    • one year ago
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    ok. you have one more equation \(x-1 = 5\), but you can handle it. Welcome.

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