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How do you solve x(3x-1)<4?

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goldsofa | Student, Grade 9 | eNotes Newbie

Posted October 14, 2012 at 9:17 PM via web

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How do you solve x(3x-1)<4?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted October 15, 2012 at 2:31 AM (Answer #1)

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The inequality x*(3x-1)<4 has to be solved.

x*(3x-1)<4

=> 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)

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terrence958 | Student , Grade 9 | Honors

Posted May 16, 2013 at 2:55 AM (Answer #4)

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x(3x-1)<4 3x^2-x<4 3x^2-x-4<0 (3x-4)(x+1)<0 don't think it would work...
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kmh23 | Student , Undergraduate | eNotes Newbie

Posted October 14, 2012 at 9:34 PM (Answer #2)

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

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scdesmond1 | Student , College Freshman | eNoter

Posted October 14, 2012 at 10:58 PM (Answer #3)

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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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