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)]= ?

Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given compound inequality.


Add to all sides.


Combine like terms on the left side.


Combine like terms on the right side.


Divide all sides by 4.



So our answer is


So the solution set is



And the answer in interval notation is []


Here's the graph of the solution set

Graph of the solution set

Note:
There is a closed circle at which means that we're including this value in the solution set
Also, there is a closed circle at 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


Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
-20 <= 4x - 3 <= -2.


Add 3  to all three terms of this compound inequality.

You will get an equivalent inequality


-17 <= 4x <= 1.


Divide all three terms of this inequality by 4.

You will get an equivalent inequality


 <= x <= .


It is your solution:  { x |  -4.25 <= x <= 0.25 }.

Solved.

--------------------

To see many other similar solved problems, look into the lesson
    - Solving compound inequalities
in this site.

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