The inequality x*(3x-1)<4 has to be solved.
=> 3x^2 - x < 4
=> 3x^2 - x - 4 < 0
=> 3x^2 - 4x + 3x - 4 < 0
=> 3x(x + 1) - 4(x + 1) < 0
=> (3x - 4)(x + 1) < 0
This is the case when either:
- (3x - 4) < 0 and (x + 1) > 0
=> x < 4/3 and x > -1
The solution set here is (-1, 4/3)
- (3x - 4) > 0 and (x + 1) < 0
=> x > 4/3 and x < -1
This is not possible for any value of x.
The solution of the inequality x*(3x-1)<4 is (-1, 4/3)
You would first distribut x over (3x-1) so that you get 4x-1x and then you would simplify the equation so that it is 3x<4. After that, you would divide both sides by 3. You would get x>1 1/3 as your answer and you would change the less then sign to greater than becuase you are dividing and anytime you divide with an inequality, you change the sign.
You distribute the x to everything in the parentheis and then get x by it self.