Warm-Up
Solve:
1. 7 x  3  3
2. x  1  x  7
3.  2 x  1
1/5
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 1
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SOLVING INEQUALITIES
Section 1-5
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To Graph Inequalities
Steps:
1. The variable is in front of the sign
2. Determine the sign and its symbol
3. Follow the arrow (x must be on
the left!)
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Example 1
Graph x < 3 onto the number line
-2
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-1
0
1
2
3
4
5
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7
8
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Example 2
Graph 3 < x onto the number line
Rewrite as x ≥ 3
-2
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-1
0
1
2
3
4
5
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6
7
8
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Example 3
Graph -1 < x < 3 onto the number line
-2
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-1
0
1
2
3
4
5
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6
7
8
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Intervals
•Brackets [ ] : DO include endpoints INCLUSIVE
•Parentheses ( ) : DO NOT include endpoints NOT
INCLUSIVE deals with infinity
smallest number, largest number 
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Intervals
Inequalities:
Verbal
Less Than
Sign
Open/Closed
Dot
Open Dot
Less Than or
Equal To
Greater Than
Closed Dot
Greater Than
or Equal to
Closed Dot
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Open Dot
Interval
Notation
( , )
[ , ]
( , )
[ , ]
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Example 4
Graph (-1, 3] onto the number line and write in
inequality notation.
-2
-1
0
1
2
3
4
5
6
7
8
1  x  3
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Example 5
Graph (-1, 5) onto the number line and write in
inequality notation
-2
-1
0
1
2
3
4
5
6
7
8
1  x  5
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Example 6
Given the graph below, write the expression
using interval notation and inequality notation
-2
-1
0
1
2
(1, 6]
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3
4
5
6
7
8
1  x  6
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Example 7
Given the graph below, write the expression
using interval notation and inequality notation
-2
-1
0
1
2
(1, )
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3
4
5
6
7
8
x  1
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Your Turn
Given the graph below, write the expression
using interval notation and inequality notation
-2
-1
0
1
(, 1]
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2
3
4
5
6
7
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x  1
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Example 8
Graph x – 6 < 1 onto the number line and write
it in interval notation x  6  1
6 6
x7
-2
-1
0
1
2
3
4
5
6
7
8
( , 7)
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Example 9
Graph 8 – 4(2 – x) < -2x onto the number line
and write it in interval notation
8  8  4x  2x
4 x  2 x
6x  0
x0
-2
-1
0
1
2
3
4
5
6
7
8
(, 0]
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Your Turn
Graph 4x + 7 < 2x - 3 onto the number line and
write it in interval notation
2x  7  3
2x  10
x  5
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
(, 5]
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Example 10
Graph -4x < 8 onto the number line and write it
in interval notation
Remember: When
4x  8
x  2
-2
-1
0
1
2
3
4
5
you divide by a
negative with an
inequality, you must
flip the inequality
sign!
6
7
8
[2, )
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Example 11
1
3x  4  ( x  2)
3
Graph
onto the number line and
write it in interval notation
-2
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-1
0
1
2
3
4
5
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7
8
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Recap of Different Representations
Graph:
-2
-1
0
1
2
3
Inequality Notation:
0 x4
Interval Notation:
(0,4]
4
5
6
7
8
Assignment
Page 133-134
11-15 odd, 23-37 odd, 57-63 odd
Due: Monday!
Conjugate & Complex Number WKST DUE TODAY!
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