Question 1150491
given:
rectangle length: {{{5x-6}}}
rectangle width: {{{x-1}}}
so, the area of the rectangle is:{{{(5x-6)(x-1)}}}


triangle height: {{{2x}}}
triangle base: {{{x}}}

so,  the area of the triangle is: {{{(x*2x)/2}}}->{{{x^2}}}


if the area of the rectangle is greater than the area of the triangle, we have:

{{{(5x-6)(x-1)>x^2}}}.........solve for {{{x}}}


{{{5x^2-6x-5x+6>x^2}}}

{{{5x^2-x^2-11x+6>0}}}

{{{4x^2-11x+6>0}}}.....factor completely

{{{4x^2-8x-3x+6>0}}}

{{{(4x^2-8x)-(3x-6)>0}}}

{{{4x(x-2)-3(x-2)>0}}}

{{{(x - 2) (4 x - 3)>0}}}

solutions

if {{{(x - 2)>0}}}=>{{{x>2}}}

if {{{ (4 x - 3)>0}}}=>{{{4x>3}}}=>{{{x>3/4}}}


 the set of possible values for {{{x}}}:

all {{{x>2}}}
all {{{x>3/4}}}-> using first greater number ({{{x=1}}}) will not make a statement {{{(5x-6)(x-1)>x^2}}} true; exclude {{{x=1}}}