anonymous
  • anonymous
Solve 8 + √2x less than or equal to 5?
Mathematics
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anonymous
  • anonymous
Solve 8 + √2x less than or equal to 5?
Mathematics
chestercat
  • chestercat
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zepdrix
  • zepdrix
Hey Alexis :) Is the x under the root like this? \(\large\rm 8+\sqrt{2x}\le 5\)
anonymous
  • anonymous
Yes :)
zepdrix
  • zepdrix
We have a bunch of `operations` being applied to x. We need to undo all of them in order to isolate the x. We have some addition, some multiplication, some square root. We'll undo all of that by starting with the most basic. We have an 8 being added, how do we undo that? :O Reverse of addition?

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anonymous
  • anonymous
We would subtract 8
anonymous
  • anonymous
From both sides
zepdrix
  • zepdrix
Mmm k good. That's a good start.\[\large\rm 8+\sqrt{2x}-8\le 5-8\]\[\large\rm \sqrt{2x}\le -3\]Hmm the multiplication is `inside` of the root, so we can't get to that operation quite yet. How do we deal with the square root? What is the opposite of square rooting? :O
anonymous
  • anonymous
We would square the number by itself to isolate it out?
zepdrix
  • zepdrix
Good, squaring is the inverse of square rooting. Think back to what you did to undo addition. You applied subtraction `to both sides`. We'll simply do that with this step as well. We'll `square both sides`.
zepdrix
  • zepdrix
\[\large\rm \left(\sqrt{2x}\right)^2\le \left(-3\right)^2\]So on the left side, the square root and the square `undo` one another, In the same way that +8 and -8 undo one another. On the right side, squaring -3 gives us (-3)(-3)=9.\[\large\rm 2x\le 9\]
zepdrix
  • zepdrix
Last step?? :)
anonymous
  • anonymous
That is where I am stuck...
zepdrix
  • zepdrix
Even though you don't see a symbol, the 2 is `multiplying` the x. You need an operation that will undo multiplication.
anonymous
  • anonymous
Divide both sides by 2?
zepdrix
  • zepdrix
Good! :)\[\large\rm \frac{\cancel2x}{\cancel2}\le \frac{9}{2}\]Giving us our final result of\[\large\rm x\le \frac{9}{2}\]
zepdrix
  • zepdrix
Yayyy team \c:/
anonymous
  • anonymous
Omg! thank you so much!!!! I really appreciate your effort and time!

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