Michael J. answered • 09/18/16
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Effective High School STEM Tutor & CUNY Math Peer Leader
Since we are subtracting logs, we divide the arguments.
log2[(4 + 3x - x2) / (2x - 1)] > 1
We know that
log22 = 1 , log24 = 2 , log28 = 3
Based on this, we set the inequality
(4 + 3x - x2) / (2x - 1) > 2
Subtract 2 or 2(2x-1)/(2x-1) on both sides of the inequality to make the right side equal to zero.
[(4 + 3x - x2) - (4x - 2)] / (2x - 1) > 0
(6 - x - x2) / (2x - 1) > 0
Multiply both sides of the inequality by (2x-1).
(6 - x - x2)(2x - 1) > 0
Factor out any terms.
(3 + x)(2 - x)(2x - 1) > 0
If the zeros of this negative cubic inequality are
x = -3 , x = 1/2 , x = 2
the interval of x in which the inequality is true is
(-∞, -3)∪(1/2, 2)
The above interval is the solution to the question.
Thomas L.
one more question what does the "u" mean between the two coordinates?
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09/18/16
Michael J.
These are not coordinates. That is how write the solution in interval notation. The "u" that you speak of is the union sign. It combines each subset of intervals because there are breaks in the solution. The comma you see separate the starting and ending points of the interval.
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09/18/16
Venrand J.
I still don't understand why you have (6-x-x^2)(2x-1) after multiplying through by (2x-1)
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07/23/21
Thomas L.
09/18/16