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anonymous

  • 5 years ago

solve absolute value inequality. 4|x-7|-6≤14

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  1. anonymous
    • 5 years ago
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    4|x-7|-6≤14 4|x-7|≤20 |x-7| <= 5 x-7<= 5 or x-7<= -5 x<=12 or x<=2

  2. anonymous
    • 5 years ago
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    how did you get 20?

  3. anonymous
    • 5 years ago
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    4|x-7|-6≤14 add 6 to both sides 4|x-7|≤20

  4. anonymous
    • 5 years ago
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    devide both sides by 4 |x-7| <= 5

  5. anonymous
    • 5 years ago
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    why do you divide by 4?

  6. anonymous
    • 5 years ago
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    cuz i see 4|x-7|≤20 and i want to isolate x eventually therfore im interested in |x-7| on the left side.

  7. anonymous
    • 5 years ago
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    i have 4 * |x-7| on the left side...im only interested in |x-7| so i hav to devide the left side by 4...since we devide the left side by 4, we HAVE to devide the right side by 4

  8. anonymous
    • 5 years ago
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    ok, i see. how did you get x-7≤ 5 or x-7≤ -5? how'd you get the -5?

  9. anonymous
    • 5 years ago
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    by definition, if |x| = A x = A or x = -A

  10. anonymous
    • 5 years ago
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    cuz when u take the absolute value of A, it is A and when u take the absolute value of -A, it is A This 'A' can be any real number

  11. anonymous
    • 5 years ago
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    so theres two answers then? x≤12 and x≤2

  12. anonymous
    • 5 years ago
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    yes. x≤12 OR x≤2

  13. anonymous
    • 5 years ago
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    ok, if i was to graph the solution, how would i?

  14. anonymous
    • 5 years ago
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  15. anonymous
    • 5 years ago
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    i drew a line at x=2, the red vertival line..and just shaded the area (that is left side in this case) x<=2

  16. anonymous
    • 5 years ago
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    do the same for x<=12 draw a line at x=12, and shade the less than area, that is left side

  17. anonymous
    • 5 years ago
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    ok, i see. thank you.

  18. anonymous
    • 5 years ago
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    I think that is wrong^ :|

  19. anonymous
    • 5 years ago
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    |x-7|<=5 -5<= (x-7) <= 5 2<= x <= 12 CORRECT that is different from the other person answer

  20. anonymous
    • 5 years ago
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    also, if the answer was x<=12 or x<=2 then you would merge both the solutions to just x<=12, bec ause that is where they both hold, BUT REMEMBER THAT ANSWER IS INCORRECT , corrrect answer is above

  21. anonymous
    • 5 years ago
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    EDIT: you would merge them to x<=2

  22. anonymous
    • 5 years ago
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    thanks

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