greatchap wrote:

Hi Guys,

I am studying topic Inequalities and have been facing few problems. I will be glad if anyone can tell me what fundamental mistake am I making.

Q1. What is the solution set of inequality 4 / (x-2) < 2 ?

(a) x > 4

(b) x < 4

(c) x < 4 union x > 4

(d) x < 2 union x > 4

(e) infinity

Correct ans is (d)

I am getting (a)

what am I doing wrong ?

Q2. Solve x^2 + 8x + 7 < 0

OA is -7< x < -1

When I try to solve I do -

(x+1) (x+7) < 0

x + 1 < 0

x < -1

And

x + 7 < 0

x < -7.

something wrong??

Similarly -

Q3 Solution of inequality -x^2 + 5x - 6 < 0

ans???

Please help me out here...

Thanks,

Cheers,

JG

here is what's important: solution of (x-a)*(x-b) > 0 (where a < b) is {x < a} U {x > b} , consequently solution of < 0 is a < x < b.

let's look at the first problem 2/(x-2) < 1 //multiply both sides by [(x-2)^2]/2 - positive number - inequality sign doesn't change

2*(x-2) < x^2-4*x + 4 -> x^2-6*x + 8 > 0 -> a = 2, b = 4

solution: { x < 2} U {x > 4} -> D

Second problem:

x^2 + 8*x + 7 < 0 -> a = -7, b = -1 -> -7 < x < -1

Third problem:

-x^2 + 5*x - 6 < 0

x^2 - 5*x + 6 > 0

a = 2, b = 3 -> {x < 2} U {x > 3}