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https://prnt.sc/ovame1

 Aug 20, 2019
 #1
avatar+102913 
+1

5 - x

______  ≥  3         subtract 3  from both sides   

4x + 1

 

 

5 - x

_____  -  3   ≥   0        get a common denominator

4x + 1

 

 

5 - x  -  3 ( 4x + 1)

_______________    ≥   0

   4x + 1 

 

 

5 - x  -  12x  - 3

____________   ≥  0

     4x  + 1 

 

 

-13x  + 2

_______      ≥   0

  4x  +  1 

 

 

We need to  solve these two  equations

 

-13x + 2  =  0                 4x  + 1  = 0

 

2  = 13x                         4x  = - 1

 

2/13   = x                        x  = -1/4

 

We have three possible itervals that will solve the original equation

 

(-inf, -1/4 )    or  ( -1/4, 2/13]   or   [ 2/13, inf)

 

If  we pick an x value in  (-1/4, 2/13]   , say x =0,    we find that

 

5 - 0                  5

_______  =      __    =     5      which makes the original inequality true

4(0) + 1             1

 

So....the solution is  (-1/4, 2/13 ] 

 

 

cool  cool   cool

 Aug 21, 2019
 #2
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+1

very much appreciared thank you so much!

 Aug 21, 2019

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