Inequality Solution [ , +Part solution included]

[lovemake1]

Inequality Solution [URGENT, +Part solution included]

Homework Statement

l 3/(x-1) - 5 l < 4

Homework Equations

The Attempt at a Solution

so here's where I am abit confused. since the inequality sign is not > or >= but instead in this case it is <. Therefore, x has to be between two numbers.

But when i tried to solve l 3/(x-1) - 5 l < 4, it doesn't work out.
Heres my work:

-4 < 3/(x-1) - 5 < 4
1 < 3/(x-1) < 9
x-1 < 3 < 9x-9

you see.. this is nothing where its suppose to be.
i end up getting... bigger number < x < smaller number

am i going the wrong way? please help !

 

[JThompson]

Use the fact that if
$$a < \frac{1}{x} < b$$

then

$$\frac{1}{a} > x > \frac{1}{b}$$ .

 

[lovemake1]

well here's a better question.

can i make the equation like this ?

1 < 3(x-1) < 9
x-1<3 or 3<9x-9
x < 4 or x > 4/3

Can this work too? 4/3 < x < 4

 

[JThompson]

You can do that, but that method will be confusing if you ever work with inequalities that have unknowns instead of numbers.

 

[JThompson]

Clarification:

$$a<\frac{1}{x}<b$$
$$\implies\frac{1}{a}>x>\frac{1}{b}$$

is only necessarily true if a and b are both negative or both positive. Sorry for the error.

 

[Mark44]

Why are you starting a new thread for a problem you have in another thread (https://www.physicsforums.com/showthread.php?t=431355)?