SOLUTION: -20 ≤ 4x -3 ≤ -2 What is the solution {x∣?? ≤ x ≤ ??} SIMPLIFY 1[-83 - (54 - 87)]= ?

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Question 148483: -20 ≤ 4x -3 ≤ -2
What is the solution {x∣?? ≤ x ≤ ??}


SIMPLIFY
1[-83 - (54 - 87)]= ?
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

-20+%3C=+4x+-3+%3C=+-2 Start with the given compound inequality.


-20%2B3%3C=4x%3C=-2%2B3 Add 3 to all sides.


-17%3C=4x%3C=-2%2B3 Combine like terms on the left side.


-17%3C=4x%3C=1 Combine like terms on the right side.


%28-17%29%2F4%3C=x%3C=%281%29%2F4 Divide all sides by 4.



So our answer is -17%2F4%3C=x%3C=1%2F4


So the solution set is



And the answer in interval notation is []


Here's the graph of the solution set

drawing%28500%2C80%2C-22%2C+6%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-22%2C+6+%2C-17%2F4%2C1%2F4%29%2C%0D%0A%0D%0Ablue%28line%28-17%2F4%2C0%2C1%2F4%2C0%29%29%2C%0D%0Ablue%28line%28-17%2F4%2C0.30%2C1%2F4%2C0.30%29%29%2C%0D%0Ablue%28line%28-17%2F4%2C0.15%2C1%2F4%2C0.15%29%29%2C%0D%0Ablue%28line%28-17%2F4%2C-0.15%2C1%2F4%2C-0.15%29%29%2C%0D%0Ablue%28line%28-17%2F4%2C-0.30%2C1%2F4%2C-0.30%29%29%0D%0A%0D%0A%29 Graph of the solution set

Note:
There is a closed circle at x=-17%2F4 which means that we're including this value in the solution set
Also, there is a closed circle at x=1%2F4 which means that we're including this value in the solution set. 


1[-83 - (54 - 87)]=1[-83 - (-33)]
                  =1[-83 +33]
                  =1[-50]
                  =-50