Download Less than or equal to

Do Now 3/5/14
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Take out HW from last night.
– Text p. 463, #2-36 evens
Copy HW in your planner.
– Practice worksheet 11.4 B
In your notebook, answer the following question.
Outside of the math classroom, where have you
heard phrases such as “at least” or “no more
than”? Give examples. How would you write the
phrases mathematically?
Homework
Text p. 463, #2-36 evens
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2) isolate the variable
4) proportion
6) -81
8) 12
10) 7/6 or 1 1/6
12) 7/99
14) -9
16) 8
18) 25
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20)
22)
24)
26)
28)
30)
32)
34)
36)
-47
5
-0.75
26
1/8
4.5
87.5
5
45
Objective
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SWBAT read and write inequalities and
graph them on a number line
Section 11.4, “Inequalities”
INEQUALITIES –
mathematical sentence formed by
placing a <, ≤, >, or ≥ between two
expressions.
11 + a ≤ 121
Writing Inequalities
Symbol
Meaning
Key Phrase
<
Is less than
Fewer than,
below
≤
Is less or equal to
At most, no
more than
>
Is greater than
More than,
above
Is greater than
or equal to
At least, no
less than
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On a number line, the GRAPH OF AN
INEQUALITY is the set of points that
represent the SOLUTION SET of the
inequality.
“Less than” and “greater
than” are represented
with an open circle.
x<8
5
6
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle.
8
9
7
8
9
10
x ≥ 11
10
11
12
13
14
11
Graph each inequality
“Less than” and “greater
than” are represented
with an open circle.
x < -3
-6
-5
5
-3
-2
-1
x≥7
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle.
4
-4
6
7
8
9
10
0
Graph each inequality
7≥y
“Less than or equal to”
and “greater than or equal
to” are represented with a
closed circle.
4
5
6
7
8
9
“Less than” and “greater
than” are represented
with an open circle.
-1 < h
-4
-3
-2
-1
10
0
1
2
Write an inequality represented by the graph.
SOLUTION
The closed circle means that 8 is not a solution of
the inequality. Because the arrow points to the
left, all numbers less than 8 are solutions.
ANSWER
An inequality represented by the graph is x < 8.
Write an inequality represented by the graph.
SOLUTION
The closed circle means that – 2.5 is a solution of
the inequality. Because the arrow points to the
right, all numbers greater than – 2.5 are solutions.
ANSWER
An inequality represented by the graph is x > – 2.5.
The highest temperature recorded in the United States
was 134°F at Death Valley, California, in 1913. Use only
this fact to write and graph an inequality that
describes the temperatures in the United States.
SOLUTION
Let T represent a temperature (in degrees Fahrenheit)
in the United States. The value of T must be less than
or equal to 134. So, an inequality is T ≤ 134.
COMPOUND INEQUALITY
–
consists of two separate inequalities
joined by AND or OR.
“AND”
Compound Inequalities
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The graph of a compound inequality with AND is the
INTERSECTION of the graphs of the inequalities.
Graph x > -2
-2
-1
0
1
2
3
2
3
Graph x ≤ 1
-2
-1
0
1
Graph -2< x ≤ 1
Graph of x ≤ 1 and x > -2
-2
-1
0
1
2
3
“OR”
Compound Inequalities
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The graph of a compound inequality with OR is the
UNION of the graphs of the inequalities.
Graph x > 2
-2
-1
0
1
2
3
2
3
Graph x ≤ -1
-2
-1
0
1
Graph of x ≤ -1 or x > 2
-2
-1
0
1
2
3
Graph each compound inequality
5<y≤9
4
5
6
7
8
9
10
h > 1 or h ≤ -3
-4
-3
-2
-1
0
1
2
Graph each compound inequality
y ≤ 16 or y > 20
14
15
16
17
18
19
20
h > -3 and h ≤ 0
-4
-3
-2
-1
0
1
2
Translate the verbal phrase into an inequality. Then
graph the inequality.
All real numbers that are greater than – 2 and less
than 3.
Inequality: – 2 < x < 3
Graph:
All real numbers that are less than 0 or greater than
or equal to 2.
Inequality: x < 0 or x ≥ 2
Graph:
Homework
Practice worksheets 11.4 B & C