Precal Question?

Question

Solve the inequality:

1+2x / x-1 => 1

Intuition says that the answer is all real numbers except for one, but im having trouble showing this...

Answer 1

It is NOT all real numbers.

Try putting ONE in X... you get zero for the denominator which makes the left side undefined.

Solve the related equation:

(1+2x)/(x-1) = 1

by multiplying both sides by (x-1). You'll eventually get x= -2 (a vertical line crossing x=-2)

That makes -2 and 1 being the 'critical' number. You have to use 5 test points to prove which ones are correct range of numbers.

Test cases are:
x < -2 (pick something like x = -10)
x = -2
-2 < x < 1 (zero sounds good)
x = 1 (which you already know won't work)
x > 1 (how about 10?)

Be aware though, more than one test point *may* prove to satisify the original inequality.

Answer 2

1+2x / x-1 => 1

(1+ 2x / x-1) - 1 => 0

Find the LCD...

[1+2x - (x-1)] / (x-1) => 0

(1+2x-x+1) / (x-1) => 0

x+2 / x-1 => 0

Use the sign table...
critical points would definitely be -2 and 1..
I bet you already know how to use the sign table so there's no need for me to show it in here..


i got x <= -2 & x>1..

^_^