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sloppycanada
 one year ago
Five rational function equations to help me with, if you'd be oh so kind.
(5x+1)/x < 1
sloppycanada
 one year ago
Five rational function equations to help me with, if you'd be oh so kind. (5x+1)/x < 1

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sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435669658962:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok i have an idea but i might be wrong so hopefully this might help. https://www.khanacademy.org/math/algebra2/rationalexpressions/solvingrationalequations/v/solvingrationalequations2

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{5x+1}{x}<1\\ \frac{5x}x+\frac1x<1\\ \quad\dots\quad<1\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1the first term simplifies . . .

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1not quite, the x's in the first term dont multiply, they cancel

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Oh. Okay so 5 + 1/x <1?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1good, now the next step is to take away 5 form both sides

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1now if we multiply both sides by x . . .

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.01 = 4x So x = 1/4

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1we get 1/4 < x but this is because we assumed that x was not negative (we didn't swap the direction of inequality)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1if we had assumed that x was negative, we would have switched the direction of inequality, when we multiplied both sides by x, we would have gotten 1/4 > x

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0Okay thanks. For this next one (assuming we're good here), wouldn't I just want to find the quadratic parts?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435671020481:dw

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1im not sure what our final answer should be for the first one

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0If we used 1/4 as our answer, I get the 1 on my calculator.

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1but is x less or greater? than 1/4

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0According to the original problem, the answer (once you plug in the value for x) should be less than one.

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0So for the first question, I think the answer would just be 1/4 < x Which would mean anything smaller than 1/4 right?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1x < 1/4 says all values of x that are less than 1/4

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1If \(\dfrac{a}{b}<1\) , that is b>a hence, in your case, x > 5x+1 that gives us \(x<\dfrac{1}{4}\). Dat sit

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0So I think that would be right... let me plug in 1/5.. that equals "0" which means x < 1/4 as our final answer right?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435671952655:dw Next question, if you have time

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435672689916:dw

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1a/b <0 iff a, b are different sign. That is if a >0, then b <0 and vice versa solve for them.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435673140046:dw for this, not for the last one
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