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anonymous

  • one year ago

Solve for x: |x| − 8 = −5 Can someone explain the steps for how to solve this please?

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  1. anonymous
    • one year ago
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    the answer is 3, but if you subtract 8-5 that equals 3 which will give you the answer

  2. anonymous
    • one year ago
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    its x - 8 = -5 the five is negative tho so..

  3. anonymous
    • one year ago
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    I just want to know the steps to figuring this out cuz i know thats not the right answer sorry..

  4. mathstudent55
    • one year ago
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    First, add 8 to both sides. Can you do that?

  5. LynFran
    • one year ago
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    \[|x|-8=-5\]ok 1st step it to add 8 to both sides of the equation

  6. mathstudent55
    • one year ago
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    \(\large |x| - 8 = -~5\) \(\large ~~~~~+8~~~~~+8\)

  7. anonymous
    • one year ago
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    so 16 and 3?

  8. mathstudent55
    • one year ago
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    No. -8 + 8 = 0 -5 + 8 = 3. That is good.

  9. mathstudent55
    • one year ago
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    You end up with \(\large |x| = 3\) Ok so far?

  10. anonymous
    • one year ago
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    the 8 is not negative tho its x minus 8 equals negative 5

  11. LynFran
    • one year ago
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    example solve for x... \[|x|-7=9\]\[|x|=9+7\]\[|x|=16\]\[x=\pm 16\]

  12. mathstudent55
    • one year ago
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    In our original equation, -8 (minus eight) means subtract 8. A subtraction can always be written as the sum of the opposite. So -8 means plus the opposite of 8. \(\large |x| - 8 = -5\) \(\large |x| + (-~8) = -5\) \(\large~~~~~~~~~~+8~~~~~+8\) After adding 8 to both sides, you get: \(\large |x| = 3\)

  13. mathstudent55
    • one year ago
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    Do you understand now how we add 8 to both sides to isolate \(|x|\)?

  14. anonymous
    • one year ago
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    yea

  15. anonymous
    • one year ago
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    the options for it tho aren't just one number its one of these x = −13 and x = −3 x = 3 and x = −3 x = 3 and x = 13 No solution

  16. anonymous
    • one year ago
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    plus i dont understand how you turned minus eight into negative eight, i dont understand why you would do that cri

  17. mathstudent55
    • one year ago
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    Ok. Now we have a simple absolute value equation. On the left side we have just \(|x|\). This equals a number, 3, on the right side. Whenever you have an absolute value equation where something in absolute value signs equals a number, you separate it into two simple equations, both without absolute signs. This is the pattern. Then I'll show you with your equation. To solve the absolute value equation \(\large |x| = k\), where k is a non-zero number, solve these two equations \(\large x = k\) or \(\large x = -k\)

  18. LynFran
    • one year ago
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    heres another example ... |dw:1439778127102:dw|

  19. mathstudent55
    • one year ago
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    With your problem, the equation now is \(\large |x| = 3\) We separate it into two equations: \(\large x = 3\) or \(\large x = -3\) Since these two equations are already solved for x, that is the final solution.

  20. LynFran
    • one year ago
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    yep ^^

  21. mathstudent55
    • one year ago
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    Let's go back to the -8 part above that is still bothering you. Subtraction is defined as adding the opposite. 8 - 2 means 8 + (-2) -3 - 4 means -3 + (-4) 5 - (-7) means 5 + 7 In general, for numbers a and b, a - b means a + (-b) That is simply the definition of subtraction. In our equation, we are subtracting 8 from the absolute value of x. We can turn the subtraction of 8 into the addition of the opposite of 8. The opposite of 8 is -8, so \(\large |x| - 8 = |x| + (-8) \) Then when we add 8 to both sides to eliminate the -8 on the left side, we end up with -8 + 8 which zero. That is how we eliminate the -8 from the left side and end up with only \(\large |x|\) on the left side.

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