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Helpjebal
 one year ago
This is a sample question from my lesson.
f(x) = √(20  2x)
the lesson says the answer is x ≤ 10.
In my textbook it says "the expression under a radical may not be negative."
So, how do I change the sign and solve to get the answer above?
Helpjebal
 one year ago
This is a sample question from my lesson. f(x) = √(20  2x) the lesson says the answer is x ≤ 10. In my textbook it says "the expression under a radical may not be negative." So, how do I change the sign and solve to get the answer above?

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1You know that you can NOT take the square root of a NEGATIVE. Correct?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, so therefore the part inside the square root (the 202x), must be greater than or equal to 0. i.e: \(202x\ge0\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\color{blue}{1)}\) Add \(2x\) to both sides. \(\color{blue}{2)}\) Divide by \(2\) on both sides.

helpjebal
 one year ago
Best ResponseYou've already chosen the best response.0Oh I see! So the addition would take away the negative sign leaving us to solve for x as normal? and adding on the other side wouldn't change ≥ to ≤? like 20  2x ≥ 0 20 ≤ 2x 20/2 ≤ 2x/2 10 ≤ x?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Follow me carefully. \(\large\color{black}{ \displaystyle 202x\ge0 \\[0.5em]}\) \(\large\color{black}{ \displaystyle 202x \color{blue}{+2x}\ge0\color{blue}{+2x} \\[0.5em]}\) The \(2x\) and \(+2x\) will cancel each other out. \(\large\color{black}{ \displaystyle 20\ge2x \\[0.5em]}\) Divide both sides by 2 \(\large\color{black}{ \displaystyle 10\ge x \\[0.5em]}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, the 10 is greater than (or equal to) x. ` (Not the other way around) `

helpjebal
 one year ago
Best ResponseYou've already chosen the best response.0oh i see! i get it now! thank you so much!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1You can logically check that x is NOT greater than 10, because if you choose for example x=11, then you get: 202(11) 2022 2 and thus, since the part inside the square root can NOT be negative,, you can tell that x is NOT greater than 10.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And you can logically see why x=10, or other x values that are smaller than 10 make the square root 0 or greater than 0 (which is perfectly valid for us).

helpjebal
 one year ago
Best ResponseYou've already chosen the best response.0i never knew to check it like that. That's very good to know! thanks :)
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