Question 969763
 {{{63x-32>63/x}}}...move terms containing {{{x}}} to one side

{{{63x-63/x>32}}}...both side multiply by {{{x}}} 

{{{63x*x-63*x/x>32*x}}}

{{{63x^2-63>32x}}}

{{{63x^2-32x-63>32x-32x}}}

{{{63x^2-32x-63>0}}}...factor

{{{63x^2-81x+49x-63>0}}}

{{{(63x^2-81x)+(49x-63)>0}}}

{{{9x(7x-9)+7(7x-9)>0}}}

{{{(9x+7)(7x-9)>0}}}

solutions:

if {{{(9x+7)>0}}} then {{{x>-7/9}}}
if {{{(7x-9)>0}}} then {{{x>9/7}}}

a.) Is the point {{{x=0}}} included in the solution set of the inequality?

answer is {{{no}}} because we were looking for solutions ({{{(9x+7)(7x-9)>0}}}) greater then {{{0}}}, second of all {{{x}}} is denominator in {{{63/x}}},and
{{{0}}} is not included  EVEN if we simplify it 

b.) are the other finite end points of the interval included in the solution set?
{{{no}}}

c.) what is the solution set? (in interval notation)

({{{-7/9}}},{{{0}}}) U ({{{9/7}}},{{{infinity}}})