How do you solve 4( x ^ { 2} - 1) < 4x - 1?

2 Answers
Aug 28, 2017

-1/2< x<3/2

Explanation:

4(x^2-1)<4x-1iff4x^2-4<4x-1iff

4x^2-4x-3<0iff4(x+1/2)(x-3/2)<0iff

(x+1/2)(x-3/2)<0iff-1/2< x<3/2

Aug 28, 2017

-1/2 < x < 3/2

Explanation:

4 (x^2 - 1) < 4x - 1
4x^2 - 4 = 4x - 1
4x^2 - 4x - 4 + 3 = 0
4x^2 - 4x - 3 = 0
Factorize
(2x + 1)(2x - 3) = 0
2x + 1 = 0 or 2x - 3 = 0
x = (-1)/2 or x = 3/2
We have
x < (-1)/2 which doesn't work in original inequality
(-1)/2 < x < 3/2 which works in original inequality
x > 3/2 it doesn't work in original inequality

Thus,
The final answer is
(-1)/2 < x < 3/2

I hope I helped!