Question 131317
{{{5 - 3x > 10x - 8}}}


Add -5 to both sides:
{{{-3x>10x-13}}}


Add -10x to both sides:
{{{-13x>-13}}}


Now divide both sides by -13, but remember that if you multiply or divide both sides of an inequality by a negative number, you have to reverse the sense of the inequality.  Look at an example using specific numbers:


{{{2<3}}} is clearly a true statement, but if you multiply both sides by a -1, you get {{{-2}}} on one side and {{{-3}}} on the other side, but the 'less than' sign is no longer correct because {{{-2}}} is actually greater than {{{-3}}}.


So back to your problem:
{{{-13x>-13}}}


Divide by -13 and turn the inequality sign around:
{{{x<1}}}


So your number line graph should have the open circle at 1, but the arrow needs to go to the left (in the negative direction).


So, let's prove the answer with a couple of examples.  0 is less than 1, so let's substitute 0 for x into the original inequality:


{{{5 - 3(0)> 10(0) - 8}}}
{{{5>-8}}}, which is a true statement.  So far, so good.


2 is greater than 1, so plug in a 2:
{{{5 - 3(2) > 10(2) - 8}}}
{{{5 - 6 > 20 - 8}}}
{{{-1>12}}}, is most assuredly a false statement.  That's a pretty good indication that you have properly defined the solution set interval for your inequality.