Loading [MathJax]/jax/output/HTML-CSS/jax.js
Home / Aptitude Tests / Mathematics / If x is positive rea...
If x is positive real number, find the range of values for w...

If x is positive real number, find the range of values for which 13x + 12x = 2+3x6x > 14x 

A.

x > -16

B.

x > 0

C.

0 < x < 6

D.

0 < x <16

Correct answer is A

13x + 12x = 2+3x6x > 14x 

= 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 < 16 (solution) 

Case 2 (+, +) = x > 0, 6x - 1 > 0 = x > 0

x > 16

Combining solutions in cases (1) and (2) 

= x > 0, x < 16 = 0 < x < 16