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| PAGE: 136 | SET: Exercises | PROBLEM: 22 |
The graph of the inequality 
is the shaded region and boundary of the inequality is 
. To graph the boundary,First find the minimum point of the graph.
Since absolute value function can not be negative, the minimum point of the
graph is where 
.
The original function is 
.
Set original function .
(Add 1 to each side)
(Simplify) 
Next make at table, fill out the table with values for x > 1 and x < 1.
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f(x) = |x – 1| |
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x |
f(x) |
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–1 |
2 |
|
1 |
0 |
|
2 |
1 |
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3 |
2 |
To draw inequality 
follow the steps.
1. Draw a coordinate plane.
2. Plot the points.
3. Since inequality symbol is >, the boundary is not included in the solution set. Graph the boundary of the inequality 
with a dashed line.
4. To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is 
.
Substitute x = 0 and y = 0 in original inequality .
The statement is false.
4. Since the statement is false, shade the region that do not contains point .
_graph.gif)
Inequality graph is
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