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

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Question 93532: solve and graph the solution:
57 -4t is greater than or equal to 13
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
57+-4t%3E=13

-4t%3E=13-57Subtract 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


0%3C=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:
Graph of t%3C=11 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.