Section 4.4
Absolute Value Inequalities
405
Version: Fall 2007
4.4
Exercises
For each of the inequalities in
Exercises 1

10
, perform each of the following tasks.
i.
Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis.
ii.
Sketch the graph of each side of the
inequality without the aid of a cal
culator.
Label each graph with its
equation.
iii. Shade the solution of the inequality
on the
x
axis (if any) in the manner
shown in Figures 4 and 8 in the narra
tive. That is, drop dashed lines from
the points of intersection to the axis,
then shade and label the solution set
on the
x
axis.
Use setbuilder and
interval notation (when possible) to
describe your solution set.
1.

x

>
−
2
2.

x

>
0
3.

x

<
3
4.

x

>
2
5.

x

>
1
6.

x

<
4
7.

x
 ≤
0
8.

x
 ≤ −
2
9.

x
 ≤
2
10.

x
 ≥
1
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1
For each of the inequalities in
Exercises 11

22
, perform each of the following tasks.
i.
Load each side of the inequality into
the
Y=
menu of your calculator. Ad
just the viewing window so that all
points of intersection of the two graphs
are visible in the viewing window.
ii.
Copy the image in your viewing screen
onto your homework paper.
Label
each axis and scale each axis with
xmin, xmax, ymin, and ymax.
La
bel each graph with its equation.
iii. Use the
intersect
utility in the
CALC
menu to determine the points of in
tersection. Shade the solution of the
inequality on the
x
axis (if any) in the
manner shown in Figures 4 and 8 in
the narrative.
That is, drop dashed
lines from the points of intersection
to the axis, then shade and label the
solution set on the
x
axis.
Use set
builder and interval notation (when
appropriate) to describe your solution
set.
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