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anonymous

  • one year ago

solve for x: −3|2x + 6| = −12 a. x = −1 and x = −5 <--- correct answer b. no solution c. x = 1 and x = 5 d. x = −9 and x = 3

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  1. jim_thompson5910
    • one year ago
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    |dw:1434963289424:dw|

  2. jim_thompson5910
    • one year ago
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    first you can divide both sides by -3 |dw:1434963323427:dw|

  3. jim_thompson5910
    • one year ago
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    |dw:1434963334417:dw|

  4. jim_thompson5910
    • one year ago
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    |dw:1434963344378:dw|

  5. jim_thompson5910
    • one year ago
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    make sense so far?

  6. anonymous
    • one year ago
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    yes, wow thank you. i kept distributing

  7. jim_thompson5910
    • one year ago
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    so you will have |2x+6| = 4

  8. jim_thompson5910
    • one year ago
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    |2x+6| = 4 breaks down into these two equations 2x+6 = 4 or 2x+6 = -4

  9. UsukiDoll
    • one year ago
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    does the absolute value rule also apply here?

  10. UsukiDoll
    • one year ago
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    I thought.. it's 2x+6=4 or -2x-6= 4...or am I remembering this wrong?

  11. jim_thompson5910
    • one year ago
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    either way works because -2x-6 = 4 is equivalent to 2x+6 = -4

  12. UsukiDoll
    • one year ago
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    oh ok! I prefer either we have 2x+6 =4 or -2x-6=4 whew

  13. UsukiDoll
    • one year ago
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    so now all we need to do is solve for x for those equations.

  14. anonymous
    • one year ago
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    i got -5 twice???

  15. UsukiDoll
    • one year ago
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    oh there it is! For an absolute value equation, we split this equation into 2 situations. one where \[\abs 2x+6 \abs = 4\] Y U NO WORK LATEX NUGH! we have one situation where the 2x+6 is positive and another situation is the negative sign is distributed all over 2x+6

  16. UsukiDoll
    • one year ago
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    2x+ 6 = 4 -2x-6=4 should be our equations

  17. UsukiDoll
    • one year ago
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    let's start at 2x+6=4 solve for x

  18. anonymous
    • one year ago
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    x = 5

  19. anonymous
    • one year ago
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    x = -5 sorry

  20. UsukiDoll
    • one year ago
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    if x = -5 and I plug it back into the equation I have -4.. -4 doesn't equal to 4 for 2x+6=4

  21. UsukiDoll
    • one year ago
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    I need x by itself.. so what do we need to do?

  22. anonymous
    • one year ago
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    subtract 6 on both sides, then divide by 2

  23. UsukiDoll
    • one year ago
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    yeah

  24. UsukiDoll
    • one year ago
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    \[2x+6=4 \] \[2x=4-6\] \[2x=-2\]

  25. anonymous
    • one year ago
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    ohhh ok so x = -1

  26. UsukiDoll
    • one year ago
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    right so our next equation -2x-6=4

  27. UsukiDoll
    • one year ago
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    so what do we need to do to get x by itself ^^

  28. UsukiDoll
    • one year ago
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    @jillybean367 are you there? ^^

  29. anonymous
    • one year ago
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    add 6 to both sides, then multiply by 2?

  30. UsukiDoll
    • one year ago
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    yes for addition part, but no for the multiplication \[-2x-6=4\] \[-2x-6+6=4+6\] \[-2x=10\]

  31. anonymous
    • one year ago
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    divide by -2

  32. UsukiDoll
    • one year ago
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    mhm and what do we have?

  33. anonymous
    • one year ago
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    x =5 ?

  34. UsukiDoll
    • one year ago
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    close you are dividing a positive number with a negative number example \[\frac{-12}{4} = -3\]

  35. UsukiDoll
    • one year ago
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    so in your problem we have \[x = \frac{10}{-2}\] or \[x = \frac{-10}{2}\]

  36. UsukiDoll
    • one year ago
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    what is x?

  37. anonymous
    • one year ago
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    5?

  38. UsukiDoll
    • one year ago
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    the answer has a negative sign though...

  39. UsukiDoll
    • one year ago
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    we can't drop the negative sign.

  40. anonymous
    • one year ago
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    oh. so its x = -5?

  41. UsukiDoll
    • one year ago
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    yes, so we have x = -1 and x = -5 if you plug those values back in the original equation you will have -12=-12 so those are the correct x values

  42. anonymous
    • one year ago
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    Wow thank you so much!

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