Solve the open sentence and graph the solution set.
|8-(w-1)| £ 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 £
as for < and rule 2 is the same for ³ as for >.
|8-(w-1)| £ 9
Rule 1 applies, so
-9 £ 8-(w-1) £ 9
-9 £ 8-w+1 £ 9
-9 £ 9-w £ 9
Add -9 to all three sides:
-9-9 £ 9-w-9 £ 9-9
-18 £ -w £ 0
Divide through by -1, which
reverses the inequality symbols:
18 ³ w ³ 0
This can be written as
0 £ w £ 18
The graph is
-------·=====================================================·------
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
which in interval notation is [0, 18]
Edwin
