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}