Question

Find the set given by the values of x satisfying simultaneously

Answer 1

\[x(x-1)>0 and \frac{ x }{ 5 }(x-2)\le0\]

Answer 2

I did

i) for x(x-1)>0

x>0 and x-1>0 => x>1

AND

x/5 >=0 which implies x>=0
also 2>=x





AND

ii)

x<0 and x<1

Also for other side
x<=0 and x>=2

Answer 3

looks good

Answer 4

\[x(x-1)>0\\
\implies x>0\quad \&\quad x-1>0\qquad{\rm OR}\qquad x<0\quad\&\quad x-1<0\\
x>1\qquad{\rm OR}\qquad x<0
\]

Answer 5

which of this is simultaneously satisfied with this:
\[
x(x-2)\le0\\
\implies x\le0\quad\&\quad x-2\ge0\qquad{\rm OR}\qquad x\ge0\quad\&\quad x-2\le0\\
\implies x\in[0,2]
\]

Answer 6

comparing them both,
we find our domain of "x" as
\[\Large x\in(1,2]\implies1<x\le2\]

Answer 7

I dont understand the last bit and the part where you got
x(x-2)<=0, is that supposed to be (x/5)(x-1)?

Answer 8

multiply both sides by "5"

Answer 9

\[\cancel{5}\times{x\over\cancel{5}}(x-2)\le0\times5\]

Answer 10

lol i did that in my working out,

I understand now thanks!!! makes so much sense!