Signs of Inequality

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1. Signs of Inequality
Term Definition Example
gt Greater than x gt 2 x is greater than 2
lt Less than x lt 1 x is less than 1
Greater than or equal to x 2 x is greater than or equal to 2
Less than or equal to x 1 x is less than or equal to 1
On a number line Open Circles mean gt or
lt Shaded Circles mean or
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2. Graphing Inequalities Simple Inequalities
Examples
greater than
X is ____________ -1
a) X gt -1
less than
X is ____________ 3
b) X lt 3
greater than or equal to
c) X 1
X is ____________ 1
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2. Graphing Inequalities Compound Inequalities
Examples
b) -4 lt a 4
c) a 1 OR a 3
d) -2 c lt 3
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3. Solving Linear Inequalities

• Linear inequalities are inequalities with more
  than one term
• Ex 2x 5 gt 11
• We solve linear equalities exactly the same as
  linear equations EXCEPT
• The direction of the inequality changes when
  multiplying or dividing by negative numbers

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3. Solving Linear Inequalities Examples
Ex 1 -3x 5 gt 26
- 5 -5
-3x gt 21
-3 -3
THE INEQUALITY CHANGED DIRECTION
x lt -7
Check try x -10 -3(-10) 5 305 35 gt
26 CHECK!
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3. Solving Linear Inequalities Examples
Ex 2 2x 10 4x 20
- 4x - 4x .
-2x 10 20
- 10 - 10
-2x 10
-2 -2
x -5
THE INEQUALITY CHANGED DIRECTION
Check try x -10 2(-10) 10 4(-10)
20 -10 -20 CHECK!
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Example 1
3. Solving Linear Inequalities Word
Problems Examples
Your cell phone plan costs 35 plus 0.05 per
text message. What is the maximum number of
messages, t, you can send to spend less than 50?
What are we trying to find?
Maximum number of messages for bill to cost less
than 50
What do we know?
t text messages 35 plus 0.05 per text Total
cost lt 50
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Example 1
3. Solving Linear Inequalities Word
Problems Examples
Your cell phone plan costs 35 plus 0.05 per
text message. What is the maximum number of
messages, t, you can send to spend less than 50?
How do we solve it?
Did we answer the original question?
35 .05t lt 50
-35 -35
Check try t 299 35 .05(299) 49.95 lt
50 CHECK!
.05t lt 15
.05 .05
t lt 300 300 messages
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3. Graphing Linear Inequalities 2 Variables!
Ex 1 Graph this linear inequality Y gt x - 3
X Y
0

1. Treat it as an equation and graph the line by
   plotting two ordered pairs
2. The line is solid if or equal to and dotted if
   just greater or less than
3. Read from Y perspective
4. Shade under if less than
5. Shade over if greater than

-3
2
-1
TEST AN ORDERED PAIR IN THE SHADED AREA TO
CHECK!!!
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3. Graphing Linear Inequalities 2 Variables!
Ex 2 Graph this linear inequality Y -x
5

1. Treat it as an equation and graph the line by
   plotting two ordered pairs
2. The line is solid if or equal to and dotted if
   just greater or less than
3. Start where x is
4. Shade under if less than
5. Shade over if greater than

X Y
0

5
2
3
TEST AN ORDERED PAIR IN THE SHADED AREA TO
CHECK!!!
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3. Graphing Linear Inequalities 2 Variables!
Ex 3 Graph this linear inequality 2x y gt
6
X Y
0

1. Treat it as an equation and graph the line by
   plotting two ordered pairs
2. The line is solid if or equal to and dotted if
   just greater or less than
3. Read from Y perspective
4. Shade under if less than
5. Shade over if greater than

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2
2
TEST AN ORDERED PAIR IN THE SHADED AREA TO
CHECK!!!
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Ex 1 Graph this linear system Y gt x
3 y -x 5
4. Graphing Linear Systems
Y -x 5
Y gt x - 3
X Y
0

X Y
0

-3
5
2
-1
2
3
TEST AN ORDERED PAIR IN THE SHADED AREA TO
CHECK!!!

1. Graph each inequality
2. The common shaded area is the solution