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Sec 5-5: Inequalities in One Variable Notes
Name: ___________________
HW: 5.5 pg. 308 #1-4
An INEQUALITY is a statement that says that one quantity is less than or greater than another.
Less than
Less than or equal to



Greater than

Greater than or equal to
STEP 1: Use these examples to write inequalities
Everyday Phrase
Translation
At least 6 glasses
The number of glasses is greater than or equal to 6
Inequality
Below 40◦
At most $10
Between 60◦ and 70◦
The temperature is less than 40◦
The price is less than or equal to $10
The temperature is greater 60 and less than 70
Everyday Phrase
Translation

glasses 6
Temperature < 40◦
Price  10
◦
60
temperature  70◦
Inequality
At least $12
Below $5
At most $15
Between $5 and $20
STEP 2: Use these examples to determine whether the number on the number line makes the inequality
a TRUE statement or a FALSE statement.
Inequality
Select a point
Test the inequality
x  2  10
x=9
9  2  10
x  2  10
x=5
11  10
5  2  10
x  2  10
x=8
7  10
8  2  10
10  10
The inequality is true
or false? Explain
True since 11 is
greater than 10
False since 7 is NOT
greater than 10
True since 10 is equal
to 10
You complete this table by looking at the example on the previous page.
Inequality
Select a point
Test the inequality
The inequality is true
or false? Explain
x=7
2x  2  8
2x  2  8
x=1
2x  2  8
x=5
How does your answer change if you make the inequality strictly less than in the last example?
x=5
2x  2  8
STEP 3: Graphing inequalities with ONE variable. We draw an arrow on the number line to
represent all the solutions of x that make the inequality true. Compare each example of inequality
graphs and describe the differences.
Inequality
Graph
x5
x5
(a) Describe the difference in the graphs for the one with the
 when compared with the one with the

inequality sign. (Hint: when do you use an open versus a closed circle on the graph?)
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Inequality
Graph
x  7
x  7
(b) Describe the difference in the graphs for the one with the
 when compared with the one with the

inequality sign. (Hint: when do you draw the arrow to the right? When do you draw the arrow to the left?)
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Use the two inequalities graphed below to answer questions c, d and e below.
Inequality
Graph
2  x  4
x  4 or x  2
(c) Use words to describe the kind of x-values that make the inequality 2  x  4 true.
(d) Use words to describe the kind of x-values that make the inequality x  4 or x  2 true.
(e) When all the solutions are between two points you have one inequality statement, like 2  x  4 .
When solutions go in opposite directions you need two separate inequality statements like ,
x  4 or x  2
Write an inequality that says the numbers are between 5 and 10. ____________
Write two inequalities that say the numbers are either less than 5 or greater than 10. ___________
STEP 4: Graph the following inequalities. Be sure to use a solid or open circle correctly. Be sure to
draw your arrow in the correct direction. You can always select a point that is shaded to make
sure that number makes the inequality true.
Inequality
x  3
x  3
5  x  2
x  2 or x  5
Graph