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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 distribute the x to everything in the parentheis and then get x by it self.
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.
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