A few days ago
vn07

Precal 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…

Top 2 Answers
A few days ago
tkquestion

Favorite Answer

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.

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A few days ago
dengshii_0515
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..

^_^

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