Solve Linear Inequalities

1
Lesson 1-6
Solve Linear Inequalities
Objective At the end of this lesson, you will be
able to solve simple and
compound inequalities.
Key Vocabulary Linear Inequality can be
written in the form axb lt c , axb
gt c , axb c and axb c
Solution of an inequality in one variable a
value when substituted for the
variable, results in a true
statement. Compound Inequalities A
compound inequality consists of two
simple inequalities joined by
and or or. Equivalent Inequalities
inequalities with the same
solution/s.
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EXAMPLE 1
Graph simple inequalities
a. Graph x lt 2.
3
EXAMPLE 1
Graph simple inequalities
b. Graph x 1.
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EXAMPLE 2
Graph compound inequalities
a. Graph 1 lt x lt 2.
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EXAMPLE 2
Graph compound inequalities
b. Graph x 2 or x gt 1.
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for Examples 1 and 2
GUIDED PRACTICE
7
for Examples 1 and 2
GUIDED PRACTICE
8
for Examples 1 and 2
GUIDED PRACTICE
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EXAMPLE 3
Solve an inequality with a variable on one side
Solve 20 1.5g 50.
20 1.5g 50
Write inequality.
1.5g 30
Subtract 20 from each side.
g 20
Divide each side by 1.5.
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EXAMPLE 4
Solve an inequality with a variable on both sides
Solve 5x 2 gt 7x 4. Then graph the solution.
5x 2 gt 7x 4
Write original inequality.
2x 2 gt 4
Subtract 7x from each side.
2x gt 6
Subtract 2 from each side.
Divide each side by 2 and reverse the inequality.
x lt 3
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for Examples 3 and 4
GUIDED PRACTICE
Solve the inequality. Then graph the solution.
5. 4x 9 lt 25
7. 5x 7 6x
6. 1 3x 14
8. 3 x gt x 9
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EXAMPLE 5
Solve an and compound inequality
4 lt 6x 10 14
Write original inequality.
4 10 lt 6x 10 10 14 10
Add 10 to each expression.
6 lt 6x 24
Simplify.
1 lt x 4
Divide each expression by 6.
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EXAMPLE 6
Solve an or compound inequality
SOLUTION
A solution of this compound inequality is a
solution of either of its parts.
First Inequality
Second Inequality
3x 5 11
5x 7 23
Write first inequality.
Write second inequality.
3x 6
5x 30
Add 7 to each side.
Subtract 5 from each side.
x 6
Divide each side by 5.
x 2
Divide each side by 3.
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EXAMPLE 6
Solve an or compound inequality
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for Examples 5,6 and 7
GUIDED PRACTICE
Solve the inequality. Then graph the solution.
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for Examples 5,6 and 7
GUIDED PRACTICE
Solve the inequality. Then graph the solution.
12. 3x 1lt 1 or 2x 5 11
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For Grade
Practice Work
Workbook pages 11 12 ( 2-22 even)
Homework
Textbook pages 44-45 ( 2-48 even)