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# Solve the inequality

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70
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3|4-5x| less than or equal to 9

DarkKnight  Jun 12, 2017
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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

CPhill  Jun 12, 2017

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