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3|4-5x| less than or equal to 9

DarkKnight  Jun 12, 2017
 #1
avatar+87336 
+2

 

Let's solve this and find out what the solutions are

 

3 l 4 - 5x l  = 9

 

3|4-5x| = 9      divide both sides by  3

 

[ 4 - 5x l =  3

 

Note that we have that  either

 

4 -  5x  =  3              or that                       4 - 5x  =  -3

 

Subtract 4  from  both sides

 

-5x =  -1                                                  -5x    -7

 

Divide both sides by  -5 

 

x  =  1/5                                                  x   = 7/5

 

Our  solution   will either lie on  [ 1/5, 7/5 ]  or outside of this interval

 

Test an x value outside this interval in the original inequality to see if it makes the inequality true, or not.....I'll pick 0

 

3 l 4 - 5(0) l ≤ 9

 

3 l 4 l    ≤ 9

 

12 ≤  9

 

This is false......so.....the solution  comes from  [ 1/5, 7/5 ]

 

Both endpoints are included because of the " ≤ "  sign

 

 

cool cool cool

CPhill  Jun 12, 2017

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