How do you solve the equation l2-3xl> 4 in the real number system?Its supposed to be the absolute value of 2 minus 3x greater than or equal to 4.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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l2-3xl> 4

 

First we need to define l2-3xl . l2-3xl is always positive,

when l2-3xl > 0 then l2-3xl = 2-3x

Then 2-3x > 0 nad it gives 2/3 > x

 

when l2-3xl < 0 then l2-3xl = -(2-3x)

Then -(2-3x)>0 and it gives x > 2/3

 

So when x<2/3 then l2-3xl = 2-3x and when x>2/3 then l2-3xl = -(2-3x)

 

l2-3xl> 4

When `x<2/3`

`(2-3x)>4`

   `2-4 > 3x`

     `-2/3 > x`

 

When` x>2/3`

`-(2-3x)>4`

        `3x > 4+2`

          `x > 2`

 

So the answers for the inequality is;

`x<-2/3 and x>2 `

`x in (-oo,-2/3) U (2,oo) `

 

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