from Al Ain to Dubai. But, his car stuck on the highway within 5
km from a mileage marker of 60 km.
This means that your friend must be somewhere between 55 km
and 65 km.
This is an example of an
absolute-value inequality.
Absolute-value inequality
are in one of the two forms:
ǀ
x
–
a
ǀ
< b
or
ǀ
x
–
a
ǀ
> b
To solve
ǀ
x
–
60
ǀ
< 5, we use
–
5 < x
–
60 < 5
11

2.8.2: Solve an Absolute-Value Inequality
For any positive p, if
ǀ
x
ǀ
≤
p,
then
–
p
≤
x
≤
p
–
p
p
Examples:
Solve the following inequality; then graph the
solution set.
a)
ǀ
x
–
5
ǀ
< 9
b)
ǀ
5
–
3x
ǀ
≤
6
12

2.8.2: Solve an Absolute-Value Inequality
For any positive p, if
ǀ
x
ǀ
≥
p,
then
x
≤
–
p
or
x
≥
p
–
p
p
Examples:
Solve the following inequality; then graph the
solution set.
a)
ǀ
x
–
7
ǀ
> 19
b)
ǀ
x
–
5
ǀ
≥
18
13

8.3: Systems of Linear Inequalities in Two Variables
The solution set of systems of linear inequality is all ordered
pairs that satisfy both inequalities.
The graph of the solution set of a system of linear
inequalities
is then the intersection of the graphs of the
individual inequalities.
Example:
Solve the following system of linear inequalities by
graphing.
x + y > 4
x
–
y < 2
14

8.3: Systems of Linear Inequalities in Two Variables
Solution:
We start by graphing each inequality separately. The
boundary line is drawn, and using (0, 0) as a test point, we see
that we should shade the half-plane above the line in both
graphs.

#### You've reached the end of your free preview.

Want to read all 20 pages?

- Fall '18
- jane
- Accounting, Elementary algebra, Negative and non-negative numbers, Binary relation