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# Find all solutions x of the inequality

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Find all solutions  x of the inequality

5/24 + |x - 1/3| < 5/16.

Nov 16, 2020

#2
+114221
+1

5/24  +  l x - 1/3 l  <   5/16       subtract  3/24  from  both  sides

l x - 1/3 l   <   5/16  - 5/24       get a common  denominator (48) on the right

l x - 1/3 l  <  15/48 - 10/48

l x - 1/3 l  <  5/48

We have two equations here

x - 1/3   <   5/48                     x - 1/3   >  -5 / 48

x <  5/48 + 1/3                     x >  -5/48 + 1/3

x <  5/48 + 16/48                 x >  -5/48 + 16/48

x <  21/48                           x  >   11/48

x <  7/16

So the solution is       11/48 < x < 7/16

Nov 16, 2020

#1
0

Convert entire equation to common denominator 48

10/48  + |x-16/48| < 15/48    subtract 10/48 from both sides of the equation

|x-16/48| < 5/48       now solve the following

x -16/48 < 5/48        or     x - 16/48 > 5/48

x < 21/48                          x > 21/48                 you should be able to take it from here....

Nov 16, 2020
#2
+114221
+1

5/24  +  l x - 1/3 l  <   5/16       subtract  3/24  from  both  sides

l x - 1/3 l   <   5/16  - 5/24       get a common  denominator (48) on the right

l x - 1/3 l  <  15/48 - 10/48

l x - 1/3 l  <  5/48

We have two equations here

x - 1/3   <   5/48                     x - 1/3   >  -5 / 48

x <  5/48 + 1/3                     x >  -5/48 + 1/3

x <  5/48 + 16/48                 x >  -5/48 + 16/48

x <  21/48                           x  >   11/48

x <  7/16

So the solution is       11/48 < x < 7/16

CPhill Nov 16, 2020