System of inequalities

[mathwannabe]

Hello everybody

I really need to know if I did this right, but I have nowhere to check my answer:

1) How many whole numbers for X satisfy the following system of inequalities:

\(\displaystyle \dfrac{x+8}{x+2}>2\)

and

\(\displaystyle \log_{10}{(x-1)}<1\)

For the first inequality I found that \(\displaystyle -2<x<4\) and for the second one \(\displaystyle 1<x<10\). So the intersection of those two would be \(\displaystyle 1<x<4\).

There are two whole numbers for X that satisfy the system.

 

[Deleted member 4993]

Hello everybody

I really need to know if I did this right, but I have nowhere to check my answer:

1) How many whole numbers for X satisfy the following system of inequalities:

\(\displaystyle \dfrac{x+8}{x+2}>2\)

and

\(\displaystyle \log_{10}{(x-1)}<1\)

For the first inequality I found that

\(\displaystyle -2<x<4\) and for the second one

\(\displaystyle 1<x<10\).

That should be 1 < x < 11

So the intersection of those two would be \(\displaystyle 1<x<4\).

There are two whole numbers for X that satisfy the system.

Correct - except as shown

 

[mathwannabe]

Correct - except as shown

Yes, thank you for pointing that out. I did it like that on the paper, I must have made a mistake when I was typing it