Porisma

A hint to get started

Transfer a rational inequality to logarithmic inputs

(i) Without using a calculator, solve the inequality 5x−1x2+x−6≤1\dfrac{5x-1}{x^2+x-6}\leq1. marks

(ii) Hence solve the inequality 1+1−5ln⁡x(ln⁡x)2+ln⁡x−6≥01+\dfrac{1-5\ln x}{(\ln x)^2+\ln x-6}\geq0. marks

[2013/YJC/I/4]

CJC · Review Problems · Question 3

Move all terms to one side and identify zeros and forbidden denominator inputs before choosing intervals.

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