Question 75787
<pre><font size = 5><b>
Solve the open sentence and graph the solution set. 
|8-(w-1)| <font face = "symbol">£</font> 9

Rules for removing absolute values in inequalities:

1.   |EXPRESSION| < A , where A is positive

is equivalent to:

    -A < EXPRESSION < A

2.   |EXPRESSION| > A , where A is positive

is equivalent to:

EXPRESSION < -A  OR  EXPRESSION > A 

Rule 1 is the same for <font face = "symbol">£</font>
as for < and rule 2 is the same for <font face = "symbol">³</font> as for >.

|8-(w-1)| <font face = "symbol">£</font> 9

Rule 1 applies, so

-9 <font face = "symbol">£</font> 8-(w-1) <font face = "symbol">£</font> 9

 -9 <font face = "symbol">£</font> 8-w+1 <font face = "symbol">£</font> 9

  -9 <font face = "symbol">£</font> 9-w <font face = "symbol">£</font> 9

Add -9 to all three sides:

  -9-9 <font face = "symbol">£</font> 9-w-9 <font face = "symbol">£</font> 9-9
    
    -18 <font face = "symbol">£</font> -w <font face = "symbol">£</font> 0

Divide through by -1, which
reverses the inequality symbols:

     18 <font face = "symbol">³</font> w <font face = "symbol">³</font> 0

This can be written as

     0 <font face = "symbol">£</font> w <font face = "symbol">£</font> 18

The graph is<font size = 3>

-------<font face = "symbol">·</font>=====================================================<font face = "symbol">·</font>------
-2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20    
</font>
which in interval notation is [0, 18]

Edwin</pre>