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

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


   

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) 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

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

Answer by ikleyn(52803) About Me  (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


-17%2F4 <= x <= 1%2F4.


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

Solved.

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

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