Question 336577
{{{abs(3pi -7)}}}{{{""+""}}}{{{abs(7pi -26)}}}
<pre><b>
To remove absolute value bars, you

1. Decide whether what is between the absolute value bars is a positive
number or a negative number.
2. If it is a positive number, simply replace the absolute value bars by
parentheses.
3. If it is a negative number, replace the absolute value bars by  
parentheses BUT PUT A - SIGN IN FRONT.

Between the absolute value bars of {{{abs(3pi -7)}}}, we have
{{{3pi -7}}}.  We know that {{{pi}}} is approximately 3.14, so we
substitute 3.14 for {{{pi}}} and see whether that is a positive number 
or a negative number:

{{{3(3.14) -7=9.42-7=2.42}}}.  That is a positive number.  Now we don't
want to use 2.42 because that is only approximate.  We just did that
to find out whether {{{3pi -7}}} is positive or negative.  We found out
that it is positive. So step 2 applies:

We just replace the absolute value bars by parentheses and so far we have:

{{{(3pi -7)}}}{{{""+""}}}{{{abs(7pi -26)}}}

Between the absolute value bars of {{{abs(7pi -26)}}}, we have
{{{7pi-26}}}.  We know that {{{pi}}} is approximately 3.14, so we
substitute 3.14 for {{{pi}}} and see whether that is a positive number 
or a negative number:

{{{7(3.14)-26=21.98-26=-4.02}}}.  That is a negative number.  Now we don't
want to use -4.02 because that is only approximate.  We just did that
to find out whether {{{7pi -26}}} is positive or negative.  We found out
that it is negative. So step 3 applies:

We replace the absolute value bars by parentheses BUT WE PUT A - SIGN IN 
FRONT.

{{{(3pi -7)}}}{{{""+""}}}{{{-(7pi -26)}}}

To keep two signs from coming together, we put brackets around the
second - sign and the parentheses:

{{{(3pi -7)}}}{{{""+""}}}{{{"["}}}{{{-(7pi -26)}}}{{{"]"}}}

Now we remove the parentheses inside the brackets:

{{{(3pi -7)}}}{{{""+""}}}{{{"["}}}{{{-7pi +26}}}{{{"]"}}}

Now we remove the parentheses and the bracket:

{{{3pi -7-7pi +26}}}

Collect like terms:

{{{-4pi+19}}}

or so it won't begin with a -, make it

{{{19-4pi}}}

Edwin</pre>