Unizor - Algebra - General Inequalities - Problems 2
Channel: Zor Shekhtman on UNIZOR Education
Date: 2013-06-17

Solve the following inequalities in the domain of real numbers.
Always establish a set of allowed values for solutions and make sure to reject the solutions you obtain that do not belong to this set.
Perform carefully non-invariant transformations in order not to loose any solutions.
Usually, solutions cannot be completely checked (there may be an infinite number of them), but a few spot-checks would always help.

Problem A
5−x−25
−−−−−−−−− &ge; 0
4·x2+4·x+2
 
Problem B
(1/2)^ [(log2(x))^2] &gt; (1/8) log2(8·x)
Here log2 is a logarithm base 2.

log[2/3] (log[3/2] ((x + 1)/(x − 1)) &ge; 0
Here log[2/3] is logarithm for base 2/3 and log[3/2] is logarithm for base 2/3.