Answer :

The solution of the inequality equation are x ≥ 4  and   x ≤  -3.

The inequality equation we have been given is

            3|2x-1|≥21

The general expression for absolute value is

              |a| = {  a  , if  a≥0   and     -a ,  if a<0}

Now we will split the absolute value in two cases which are

   3|2x-1|  =  {   6x-3 ,  if x≥1/2   and     -6x + 3  , if  x<1/2}

First we will solve for the positive value, that is,

         6x-3 ≥ 21

         6x ≥ 21 + 3

         6x ≥ 24

           x ≥ 4

Then we will solve for the negative value, we get

           -6x+3 ≥ 21

            -6x ≥ 21-3

             -6x ≤ 18

                x ≤  -3

Combining both the values we will get (-∞,-3]U[4,∞)

Hence the two value of x variable will be   x ≥ 4  and   x ≤  -3.

Learn more about inequalities here : https://brainly.com/question/24372553

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