Question 93532
{{{57 -4t>=13}}}


{{{-4t>=13-57}}}Subtract 57 from both sides



{{{-4t>=-44}}} Combine like terms on the right side



{{{t<=(-44)/(-4)}}} Divide both sides by -4 to isolate t (note: multiplying/dividing a negative number on both sides flips the sign of the inequality)




{{{t<=11}}} Reduce

      
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Answer:

So our answer is {{{t<=11}}}





Now let's graph {{{t<=11}}}




Set up a number line:

{{{number_line(500,1,21)}}} note: just replace the x with the variable you are working with



Now plot the point t=11 on the number line



{{{number_line(500,1,21, 11)}}}



Now pick any test point you want, I'm going to choose t=0, and test the inequality {{{t<=11}}}



{{{0<=11}}} Plug in {{{t=0}}}



Since this inequality is true, we simply shade the entire portion in which contains the point t=0 using the point t=11 as the boundary.This means we shade everything to the left of the point t=11 like this:

{{{drawing(500,50,1,21,-10,10,
number_line(500,1,21, 11),
blue(line(11,-5,11-10,-5)),
blue(line(11,-6,11-10,-6)),
blue(line(11,-7,11-10,-7)),
blue(arrow(11,-5,11-10.2,-5)),
blue(arrow(11,-5.5,11-10.2,-5.5)),
blue(arrow(11,-6,11-10.2,-6))
)}}}  Graph of {{{t<=11}}} with the shaded region in blue

note: at the point t=11, there is an <b>closed</b> circle. This means the point t=11 is included from the solution set.