Question 683951
<pre>
Learn the four ways to eliminate absolute value bars:

1.        {{{abs(matrix(2,1,  ALGEBRAIC,EXPRESSION))}}}{{{""<""}}}{{{K}}}  is equivalent to this:  " {{{-K}}}{{{""<""}}}{{{matrix(2,1,ALGEBRAIC,EXPRESSION)}}}{{{""<""}}}{{{K}}} "

2.        {{{abs(matrix(2,1,  ALGEBRAIC,EXPRESSION))}}}{{{""<=""}}}{{{K}}}  is equivalent to this:  " {{{-K}}}{{{""<=""}}}{{{matrix(2,1,ALGEBRAIC,EXPRESSION)}}}{{{""<=""}}}{{{K}}} " 

3.        {{{abs(matrix(2,1,  ALGEBRAIC,EXPRESSION))}}}{{{"">""}}}{{{K}}}  is equivalent to this: "  {{{matrix(2,1,ALGEBRAIC,EXPRESSION)}}}{{{""<""}}}{{{-K}}}   {{{"OR"}}}   {{{matrix(2,1,ALGEBRAIC,EXPRESSION)}}}{{{"">""}}}{{{K}}} "

4.        {{{abs(matrix(2,1,  ALGEBRAIC,EXPRESSION))}}}{{{"">=""}}}{{{K}}}  is equivalent to this: "  {{{matrix(2,1,ALGEBRAIC,EXPRESSION)}}}{{{""<=""}}}{{{-K}}}   {{{"OR"}}}   {{{matrix(2,1,ALGEBRAIC,EXPRESSION)}}}{{{"">=""}}}{{{K}}} "

Yours is case 1:

   |6x-5| < 10 is equivalent to

     -10 < 6x-5 < 10

We solve for x in the middle:

Add +5 to all three sides like this:

     -10 < 6x-5 < 10
     <u> +5     +5   +5</u>
      -5 < 6x   < 15

Dow divide all three sides by 6

      {{{(-5)/6}}} < x  < {{{15/6}}}

The fraction on the right reduces to {{{5/2}}}

      {{{(-5)/6}}} < x  < {{{5/2}}}

In interval notation that is:

         {{{(matrix(1,3,

-5/6,",",5/2))}}}
   


Edwin</pre>