Ahsome
  • Ahsome
Absolute Values
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Ahsome
  • Ahsome
Solve for:\[|x+1|\le |2x-5|\]
anonymous
  • anonymous
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.
Ahsome
  • Ahsome
But don't two cases cancel each other out though..?

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More answers

anonymous
  • anonymous
No apparently not though
anonymous
  • anonymous
|dw:1433509203824:dw|
Ahsome
  • Ahsome
Are these the posibilities? \[x+1\le 2x-5\]\[-(x+1)\le 2x-5\]\[x+1\le -(2x-5)\]\[-(x+1)\le -(2x-5)\]
anonymous
  • anonymous
|dw:1433509233981:dw|
anonymous
  • anonymous
Yes exactly, so you have to work out four of those linear inequalities for x
Ahsome
  • Ahsome
Exactly. At one point, both are negatives, so its the same as having positive on both, right?
Ahsome
  • Ahsome
Or will that affect somehow?
anonymous
  • anonymous
Just resolve them, how you would normally approach them, you will just result in four individual 'x' values
Ahsome
  • Ahsome
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?
anonymous
  • anonymous
I just briefly skimmed your working out, but other than that, the solutions can be presented as you have done them
Ahsome
  • Ahsome
I made a mistake in calculations. let me fix
IrishBoy123
  • IrishBoy123
square both sides and work as a quadratic or draw both easier
anonymous
  • anonymous
The last one, I've noticed
Ahsome
  • Ahsome
\[x+1≤2x−5\]\[x≤2x−6\]\[−x≤−6\]\[x≥6\] \[−(x+1)≤2x−5\]\[−x−1≤2x−5\]\[−x≤2x−4\]\[−3x≤−4\]\[x≥\dfrac{4}{3}\] \[x+1≤−(2x−5)\]\[x+1≤−2x+5\]\[x≤-2x+4\]\[3x≤4\]\[x\le\frac{4}{3}\] \[−(x+1)≤−(2x−5)\]\[−x−1≤−2x+5\]\[−x≤−2x+6\]\[x≤6\] Combine the like terms, the ones that have the smaller set of possible values \[x\ge6, x\le\dfrac{4}{3}\]
Ahsome
  • Ahsome
@DelTaVsPi

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