Question

solve 5x-1/x-2 < 2

Answer 1

5x-1<2x-4 this implies 3x<-3 os x<-1

Answer 2

any x less than -1 satisfies the inequality

Answer 3

Is it :
\[\frac{5x-1}{x-2}<2~~??\]

Answer 4

yes that's it

Answer 5

@blurbendy

Answer 6

this is equal to x^2 < x + 2
and if you graph this on a number line, you'll see
-1 < x <2
so x = 0
x = 1

Answer 7

5x-1/x-2<2
=>5x-1<2(x-2)
=>5x-1<2x-4
=>5x-2x<-4+1
=>3x<-3
=>x<-1

Answer 8

We have :
\[\frac{5x-1}{x-2}<2\iff \frac{5x-1}{x-2}-2<0

\\\iff \frac{5x-1-2(x-2)}{x-2}<0
\\\iff \frac{3x-3}{x-2}<0\]
So, we should study the sign of the two expression : 3x-3 and x-2. like this :
We have :
\[3x-3=0\iff x=1\]
and :
\[x-2=0\iff x=2\]
So, we make a table contains the sign like this :
\[\begin{array}{|c|lcccccr|}\hline x&-\infty&& 1&&2&&+\infty\\\hline 3x-3&&-&|&+&|&+&\\\hline x-2&&-&|&-&|&+&\\\hline \frac{3x-3}{x-2}&&+&|&-&\|&+&\\\hline \end{array}\]
And because we get "<0" in the inequality, we are looking for the negative values.
Wich means that the solution is :
\[1<x<2\]
which means :
\[\text{Soulutin Set }=\left(1,2\right)=\{x~/~ 1<x<2 \}\]

All the answers above are false and incorrect !

Answer 9

I have done a mistype !
It should be 3x+3 not 3x-3 but the method is what I have wrote !

Answer 10

but the answer is still correct right

Answer 11

we replace "1" by "-1" because :
\[3x+3=0\iff x=-3/3=-1\]

Answer 12

I am lazy to write the solution again !