Transcript Beginning Algebra Early Graphing

Section 3.5
Graphing Linear
Inequalities
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Inequalities
An inequality is a statement that describes how two
numbers are related to one another.
– 5 – 4– 3 – 2 – 1
–4<–1
0
1
2
3
4
5
–1>–4
“is greater than”
“is less than”
–4–1
–1–4
“is greater than
or equal to”
“is less than
or equal to”
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Graphing Linear Inequalities
Replace the inequality symbol by an equality symbol.
Graph the line.
a) The line will be solid if the inequality is  or .
b) The line will be dashed if the inequality is > or <.
2. Test the point (0, 0) in the inequality if (0, 0) does not
lie on the graphed line in step 1.
a) If the inequality is true, shade the region on the
side of the line that includes (0, 0).
b) If the inequality is false, shade the region on the
side of the line that does not include (0, 0).
3. If the point (0, 0) is a point on the line, choose
another test point and proceed accordingly.
1.
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Example
Graph 2x + 5y  10.
Graph the line 2x + 5y = 10.
Look for a test point.
y
The solid line
indicates that
the line is
part of the
solution.
Is (0, 0) a solution?
2x + 5y  10
2(0) + 5(0)  10
0  9 False
4
1
x
1
4
(0, 0) is not included in
the solution.
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Example
Graph y < – 3x + 9
Graph the line y = – 3x + 9.
y
The dashed
line indicates
that the line is
not part of the
solution.
Look for a test point.
Is (0, 0) a solution?
y < – 3x + 9
0 < – 3(0) + 9
4
x
4
0 < 9 True
(0, 0) is included
in the solution.
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Example
Graph x > 2.
Graph x = 2
The line will be dashed.
Test (0, 0) in the inequality.
x>2
0 > 2 false
Shade the region that does not
include (0, 0).
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