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Ahsome

  • one year ago

Absolute Values

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  1. ahsome
    • one year ago
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    Solve for:\[|x+1|\le |2x-5|\]

  2. anonymous
    • one year ago
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    In this particular question, you will have to work out for x four times. The reason is that, once you move the 'absolute signs' over the equal sign, you already have two equations to work with.

  3. ahsome
    • one year ago
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    But don't two cases cancel each other out though..?

  4. anonymous
    • one year ago
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    No apparently not though

  5. anonymous
    • one year ago
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    |dw:1433509203824:dw|

  6. ahsome
    • one year ago
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    Are these the posibilities? \[x+1\le 2x-5\]\[-(x+1)\le 2x-5\]\[x+1\le -(2x-5)\]\[-(x+1)\le -(2x-5)\]

  7. anonymous
    • one year ago
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    |dw:1433509233981:dw|

  8. anonymous
    • one year ago
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    Yes exactly, so you have to work out four of those linear inequalities for x

  9. ahsome
    • one year ago
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    Exactly. At one point, both are negatives, so its the same as having positive on both, right?

  10. ahsome
    • one year ago
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    Or will that affect somehow?

  11. anonymous
    • one year ago
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    Just resolve them, how you would normally approach them, you will just result in four individual 'x' values

  12. ahsome
    • one year ago
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    Ok. Let me solve for some \[x+1≤2x−5\]\[x\le2x-6\]\[-x\le -6\]\[x\ge 6\] \[−(x+1)≤2x−5\]\[-x-1\le2x-5\]\[-x\le 2x-4\]\[-3x\le -4\]\[x\ge \dfrac{4}{3}\] \[x+1≤−(2x−5)\]\[x+1\le -2x+5\]\[x\le2x+4\]\[-x\le4\]\[x\ge -4\] \[−(x+1)≤−(2x−5)\]\[-x-1\le -2x+5\]\[-x\le -2x+6\]\[x\le 6\] Do we just combine like terms? @DelTaVsPi?

  13. anonymous
    • one year ago
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    I just briefly skimmed your working out, but other than that, the solutions can be presented as you have done them

  14. ahsome
    • one year ago
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    I made a mistake in calculations. let me fix

  15. IrishBoy123
    • one year ago
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    square both sides and work as a quadratic or draw both easier

  16. anonymous
    • one year ago
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    The last one, I've noticed

  17. ahsome
    • one year ago
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    \[x+1≤2x−5\]\[x≤2x−6\]\[−x≤−6\]\[x≥6\] \[−(x+1)≤2x−5\]\[−x−1≤2x−5\]\[−x≤2x−4\]\[−3x≤−4\]\[x≥\dfrac{4}{3}\] \[x+1≤−(2x−5)\]\[x+1≤−2x+5\]\[x≤-2x+4\]\[3x≤4\]\[x\le\frac{4}{3}\] \[−(x+1)≤−(2x−5)\]\[−x−1≤−2x+5\]\[−x≤−2x+6\]\[x≤6\] Combine the like terms, the ones that have the smaller set of possible values \[x\ge6, x\le\dfrac{4}{3}\]

  18. ahsome
    • one year ago
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    @DelTaVsPi

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