Question 1066304
AS GIVEN and described,  {{{5x-1>5x+1}}}
and a strep from that GIVEN information is
{{{5x-1+(-5x)>5x+1+(-5x)}}}
{{{-1>1}}}-----------a false statement.  



The first THREE expressions should work this way:
{{{(5x+1)^2>(2x)^2+(4x)^2}}}


{{{25x^2+10x+1>4x^2+16x^2}}}


{{{25x^2+10x+1>20x^2}}}


{{{5x^2+10x+1>0}}}


Critical x-values:
{{{(-10+- sqrt(100-4*5*1))/(2*5)}}}


{{{(-10+- sqrt(80))/10}}}


{{{(-10+- sqrt(2*2*2*2*5))/10}}}


{{{(-10+- 4*sqrt(5))/10}}}


{{{highlight_green(-1+- (2/5)sqrt(5))}}}



--
You should check also to be sure you know what values for x will make the lengths 2x+2, 4x, and 5x+1, POSITIVE VALUES.  Note, because of 4x one of the sides,  {{{highlight_green(x>0)}}}  necessary.  


Look at {{{-1+(2/5)sqrt(5)}}};
{{{-0.105572}}}
which is the right-hand critical value of x, negative, and therefore will not work for {{{4x}}};
The values for x to the left of the left-hand critcal value will also not be acceptable, because they are negative.  The interval between the two critical x-values neither will work; the inequality will fail as well as side length 4x being negative.


SOLUTION:
{{{highlight(x>0)}}}