+0

0
87
3

Solve the inequality (x - 1)/(x + 1) > 2.

May 10, 2020

#1
+1

^m^, whymenotsmart

May 10, 2020
#2
+1

Solve the inequality:        (x - 1)(x + 1)  >  2

Multiply out:                                x2 - 1  >  2

Get one side to be zero:             x2 - 3  >  0

Factor:      [ x + sqrt(3) ] · [ x - sqrt(3) ]  > 0

The number line is now broken into 5 regions:

x < - sqrt(3)          x = - sqrt(3)          - sqrt(x) < x < sqrt(3)          sqrt(3)           x > sqrt(3)

Test each of these regions, one at a time:

-- for  x < - sqrt(3)   choose a number smaller than - sqrt(3)

I'm going to choose -10.

Does -10 work in the inequality x2 - 3  >  0   -->   (-10)2 - 3  >  0   --->   100 - 3 > 0

Yes, that's true!  So the region  x < - sqrt(3) is part of the answer.

-- for  x = - sqrt(3)   This doesn't work because there is no equal sign in the original problem.

-- for  - sqrt(x) < x < sqrt(3)   choose a number in this region

I'm going to choose 0.

Does 0 work in the inequality x2 - 3  >  0   -->   (0)2 - 3  >  0   --->   0 - 3 > 0

No, that's not true ... so this region is not part of the answer.

-- for  x = sqrt(3)   This doesn't work because there is no equal sign in the original problem.

-- for  x > sqrt(3)   choose a number greater than sqrt(3)

I'm going to choose 10.

Does 10 work in the inequality x2 - 3  >  0   -->   (10)2 - 3  >  0   --->   100 - 3 > 0

Yes, that's true!  So the region  x > sqrt(3) is also part of the answer.

So, the answer is:  either  x < - sqrt(3)  or  x > sqrt(3)

May 10, 2020
#3
0

Hello Geno,

I believe he meant $$\frac{(x-1)}{(x+1)}>2$$ Since there is "/"

Guest May 11, 2020