If x is a positive real number, find the range of values for which \( \frac{1}{3x} + \frac{1}{2} > \frac{1}{4x} \)

Assessment: JAMB UTME - Mathematics - 1998 Subject: General Mathematics

Question 1 Report

If x is a positive real number, find the range of values for which \( \frac{1}{3x} + \frac{1}{2} > \frac{1}{4x} \)

Answer Details
1 3 x  +  1 2  >  1 4 x
=  2 + 3 x 6 x  >  1 4 x
= 4(2 + 3x) > 6x = 12x2 - 2x = 0
= 2x(6x - 1) > 0 = x(6x - 1) > 0
Case 1 (-, -) = x < 0, 6x -1 < 0

= x < 0, x <  1 6  = x <  1 6  (solution)

Case 2 (+, +) = x > 0, 6x -1 > 0 = x > 0, x >  1 6
Combining solutions in cases(1) and (2)
= x > 0, x <  1 6  = 0 < x < 

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