September 13, 2012
Lesson 2.6
Solving Linear Inequalities
What are the inequality symbols for each statement?
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
A linear inequality is an inequality containing
expressions in which each variable term contains a
single variable with an exponent of one.
Which are linear inequalities? Y
Y
Y
N
Y
N
N
N
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September 13, 2012
Graphing Inequalities
•
°
°
-5
-4
-3
-2
-1
0
1
2
-5
-4
-3
-2
-1
0
1
2
-5
-4
°
-2
-1
0
1
2
-3
3
•
3
3
4
5
4
5
•
5
4
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Set-builder notation
we write
For
and we say
"The set of all real numbers
x where is greater than -10."
Interval notation
Try x ≤ -2.
Set-builder notation: {x|x ≤ -2}
Interval notation: (-∞, -2]
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To Solve Linear Inequalities
To solve linear inequalities in one variables,
1. Simplify both sides of the inequality as needed.
a) Distribute to clear parenthesis.
b) Multiply by LCD to clear fractions or decimals.
c) Combine like terms.
2. Use the addition principle so that all variable terms
are on one side of the inequality and all constant terms
are on the other side. Then combine like terms.
3. Use the multiplication principle to clear any remaining
coefficients. If you multiply by a negative you must
switch the inequality sign.
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