Transcript Do Now 12/7/06 - Howell Township Public Schools

Do Now 12/11/09
 Copy

 In
HW in your planner.
Text p. 359, #4-14 even 22-36 even.
your journal, 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?
Chapter 6 Preview
“Solving and Graphing Linear Inequalities”
(6.1) Solve Inequalities Using Addition and Subtraction
(6.2) Solve Inequalities Using Multiplication and Division
(6.3) Solve Multi-Step Inequalities
(6.4) Solve Compound Inequalities
Winter break
(6.5) Solve Absolute Value Equations
(6.6) Solve Absolute Value Inequalities
(6.7) Graph Linear Inequalities in Two Variables
Section 6.1
“Solve Inequalities Using Addition and
Subtraction”
INEQUALITIES –
mathematical sentence formed by
placing a <, ≤, >, or ≥ between two
expressions.
11 - a ≤ 121
Writing Equations with Inequalities
Symbol
Meaning
Key phrases
=
Is equal to
The same as
<
Is less than
Fewer than
≤
Is less than or equal At most, no more
to
than
>
Is greater than
More than
≥
Is greater than or
equal to
At least, no less
than
 On
a number line, the GRAPH OF AN
INEQUALITY is the set of points that
represent ALL SOLUTIONS of the
inequality.
“Less than” and “greater
than” are represented
with an open circle.
Graph 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
11
Graph x ≥ 11
10
11
12
13
14
15
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.
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.
Solving an Inequality…
Isolate the variable! Get ‘m’ by itself.
To get the ‘m’
by itself get rid of
“adding 4.”
Do the opposite.
“Subtract 4.”
m + 4 < 12
- 4 -4
Whatever you do to
one side of the Inequality
you must do the other side.
m<8
Solving an Inequality…
Isolate the variable! Get ‘n’ by itself.
To get the ‘n’
by itself get rid of
“subtracting 5.”
Do the opposite.
“Add 5.”
n-5≥ 6
+ 5 +5
Whatever you do to
one side of the inequality
you must do the other side.
n ≥ 11
Solve x – 5 > – 3.5. Graph your solution.
x – 5 > – 3.5
x – 5 + 5 > – 3.5 + 5
x > 1.5
Write original inequality.
Add 5 to each side.
Simplify.
ANSWER
The solutions are all real numbers greater
than 1.5. Check by substituting a number
greater than 1.5 for x in the original
inequality.
Solve p – 9.2 < – 5. Graph your solution.
SOLUTION
p – 9.2 < – 5
Write original inequality.
p – 9.2 + 9.2 < – 5 + 9.2
Add 9.2 to each side.
x < 4.2
Simplify.
ANSWER
The solutions are all real numbers less than
4.2. Check by substituting a number less
than 4.2 for x in the original inequality.
Solve 9 > x + 7. Graph your solution.
9≥x+7
9–7≥x+7–7
2≥x
Write original inequality.
Subtract 7 from each side.
Simplify.
ANSWER
You can rewrite 2 ≥ x as x ≥ 2.
The solutions are all real
numbers less than or equal
to 2.
Solve y + 5.5 > 6. Graph your solution.
SOLUTION
y + 5.5 > 6
Write original inequality.
y + 5.5 –5.5 > 6 –5.5
Subtract 5.5 from each side.
y > 0.5
Simplify.
ANSWER
You can rewrite 0.5 < y as y > 0.5 . The
solutions are all real numbers greater than
or equal to 0.5 .
Solve a real-world problem
LUGGAGE WEIGHTS
You are checking a bag at an airport. Bags can weigh
no more than 50 pounds. Your bag weighs 16.8 pounds.
Find the possible weights w (in pounds) that you can
add to the bag.
SOLUTION
Write a verbal model. Then write
and solve an inequality.
16.8
+
w
≤
50
Solve a real-world problem
16.8+ w < 50
16.8 + w – 16.8 < 50 – 16.8
w ≤ 33.2
ANSWER
You can add no
more than 33.2 pounds.
Write inequality.
Subtract 16.8 from each side.
Simplify.
Write and solve an inequality to find
the possible values of x.
 Perimeter
≤ 51.3 feet
14.2 + 15.5 + x ≤ 51.3
14.2 ft
29.7 + x ≤ 51.3
x ft
x ≤ 21.6
15.5 ft
Algebra in “Real-Life!”
 In
your groups, complete the “real-life”
activity.

Interdisciplinary Application “Bald Eagles”
Algebra in “Real-Life!”
 In
your groups, complete the two “real-life”
activities.

Interdisciplinary Application “Bald Eagles”
•
•
•
•
•
•
•
1) y = 393x + 14,324
2) graph
3) approximately 18,254
4) habitat loss, less people counting
5) y = 512.5x + 13,698
6) graph
7) approximately 18,880
NJASK7 Prep
24
Homework
 Text
p. 359, #4-14 even 22-36 even
Practice Worksheet Form B
#2-24 even
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2) x > -2
4) x ≥ -7
6) x ≤ -1
8) n ≤ 12
10) m < 1
12) x ≤ -7.5
14) y < 4.8
16) d > 10.2
18) m – 3 ≥ 10; m ≥ 13
20) 85 > x – 63; x > 148
22) 17 hats or less
24) a). 6532 + 4887 < 5034 + s; s > 6385
b). Yes, because 6392 > 6385. No,
because 6385 is not > 6385. No, because 6377
is not > 6385.