Question 93529
{{{-12>=24x}}}


{{{24x<=-12}}} Flip the sides so the variable is on the left side


{{{x<=(-12)/(24)}}} Divide both sides by 24 to isolate x


{{{x<=-1 / 2}}} Reduce


So our answer is {{{x<=-1 / 2}}} or {{{x<=-0.5}}} in decimal form



Start with the given inequality:


{{{x<=-0.5}}}


Now lets graph {{{x<=-0.5}}}




Start with the given inequality:


{{{x<=-0.5}}}


Now let's graph {{{x<=-0.5}}}



Set up a number line:

{{{number_line(500,-10.5,9.5)}}} 


Now plot the point x=-0.5 on the number line



{{{number_line(500,-10.5,9.5, -0.5)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x<=-0.5}}}



{{{0<=-0.5}}} Plug in {{{x=0}}}



Since this inequality is <font size=4><b>not</b></font> true, we simply shade the entire portion that does <font size=4><b>not</b></font> contain the point x=0 using the point x=-0.5 as the boundary. This means we shade everything to the left of the point x=-0.5 like this:

{{{drawing(500,50,-10.5,9.5,-10,10,
number_line(500,-10.5,9.5, -0.5),
blue(line(-0.5,-5,-0.5-10,-5)),
blue(line(-0.5,-6,-0.5-10,-6)),
blue(line(-0.5,-7,-0.5-10,-7)),
blue(arrow(-0.5,-5,-0.5-10.2,-5)),
blue(arrow(-0.5,-5.5,-0.5-10.2,-5.5)),
blue(arrow(-0.5,-6,-0.5-10.2,-6))
)}}}  Graph of {{{x<=-0.5}}} with the shaded region in blue

note: at the point x=-0.5, there is an <b>closed</b> circle. This means the point x=-0.5 is included from the solution set.