SOLUTION: solve and graph the solution: 57 -4t is greater than or equal to 13

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57+-4t%3E=13

Subtract 57 from both sides

-4t%3E=-44

Combine like terms on the right side

t%3C=%28-44%29%2F%28-4%29

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

t%3C=11

Reduce

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Answer:
So our answer is t%3C=11

Now let's graph t%3C=11

Set up a number line:
number_line%28500%2C1%2C21%29

note: just replace the x with the variable you are working with

Now plot the point t=11 on the number line

number_line%28500%2C1%2C21%2C+11%29

Now pick any test point you want, I'm going to choose t=0, and test the inequality t%3C=11

Plug in

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%28500%2C50%2C1%2C21%2C-10%2C10%2C%0D%0Anumber_line%28500%2C1%2C21%2C+11%29%2C%0D%0Ablue%28line%2811%2C-5%2C11-10%2C-5%29%29%2C%0D%0Ablue%28line%2811%2C-6%2C11-10%2C-6%29%29%2C%0D%0Ablue%28line%2811%2C-7%2C11-10%2C-7%29%29%2C%0D%0Ablue%28arrow%2811%2C-5%2C11-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%2811%2C-5.5%2C11-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%2811%2C-6%2C11-10.2%2C-6%29%29%0D%0A%29

drawing%28500%2C50%2C1%2C21%2C-10%2C10%2C%0D%0Anumber_line%28500%2C1%2C21%2C+11%29%2C%0D%0Ablue%28line%2811%2C-5%2C11-10%2C-5%29%29%2C%0D%0Ablue%28line%2811%2C-6%2C11-10%2C-6%29%29%2C%0D%0Ablue%28line%2811%2C-7%2C11-10%2C-7%29%29%2C%0D%0Ablue%28arrow%2811%2C-5%2C11-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%2811%2C-5.5%2C11-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%2811%2C-6%2C11-10.2%2C-6%29%29%0D%0A%29

Graph of

with the shaded region in blue
note: at the point t=11, there is an closed circle. This means the point t=11 is included from the solution set.