Solve ABSOLUTE VALUE equations

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

 

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

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If a picture is TOO SMALL,

Then CLICK on the PICTURE.

If a picture is TOO SMALL,

Then CLICK on the PICTURE.

 When solving an absolute value inequality, replace

the       | STUFF |         with        ± ( STUFF ),
THUS , we split the inequality into two statements,
and solve them as an      or   or     and statement.
Graph the and statements as an overlapping region,
and the or statements as two pieces going in opposite directions.

Example 1: Solve |3x-1| < 2. ----- THIS WILL BE AN AND TYPE

Replacing the   | 3x-1  |   symbols with      ± ( 3x-1 ), we see

± ( 3x-1 ) < 2       This splits into      3x-1  < 2   AND   - (3x-1) < 2

For the statement on the right, divide by -1 and reverse the < symbol.   
3x-1 < 2   and   3x-1 > -2          NOW SOLVE EACH

 x < 1   and   x >  -1/3     graph the INTERSECTION (OVERLAPPING

Example 2  Solve     | 5x - 2| > 17

Replacing the | 5x-2   | symbols with      ± ( 5x-2  ), we see

± ( 5x-2 ) > 17      This splits into      5x-2  > 17   OR   - (5x-2) > 17

For the statement on the right, divide by -1 and reverse the < symbol.

   5x-2 > 17   OR   5x-2 < -17    NOW SOLVE EACH

x > 3.8    OR   x <  -3 
  
graph the UNION ( put the two graphs together as one)