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viniterranova
 3 years ago
(x +1) / (2x) < 4
viniterranova
 3 years ago
(x +1) / (2x) < 4

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Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1first find when (x+1)/(2x)=4 or is undefined

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1you will need these values to solve the inequality

viniterranova
 3 years ago
Best ResponseYou've already chosen the best response.0May this help you.

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1yes, i know that is the question, but it is important that you solve the equation (x+1)/(2x)=4 before you solve (x+1)/(2x)<4

viniterranova
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry....but may u do it?

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1(x+1)/(2x)=4 x+1=4(2x) x+1=84x 5x=7 x=7/5 we also must know when (x+1)/(2x)=4 is undefined it is undefined at x=2, because the denominator 2x=0

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1now we can split the number line up into 3 intervals using these 2 numbers

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1first we will simplify the rational inequality

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1well i guess that's not necessary in this case, but usually you want to get 0 on one side of the inequality

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1we have the values we will use to form our intervals, x=2, x=7/5 this splits the domain of the function into the following intervals: (infinity, 7/5), (7/5, 2), (2, infinity)

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1we will pick a value at random from these intervals and see if it is less than 4. if it is, the entire interval is part of the solution

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1from the first interval we can use x=0 (0+1)/(20)<4? 1/2<4? TRUE x<7/5 is part of the solution

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1next we will pick the value 8/5 from the 2nd interval (8/5+1)/(28/5)<4? (13/5)/(2/5)<4? 13/2<4? FALSE, this is not part of solution

Dockworker
 3 years ago
Best ResponseYou've already chosen the best response.1from 3rd interval we can use x=3 (3+1)/(23)<4? 4/1<4? 4<4? TRUE x>2 is part of solution so entire solution is x<7/5 or x>2 now you see why we had to solve the related equation

viniterranova
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks for the answer
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