Transcript Solving an Inequality…

Do Now 11/11/09
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Take out HW from yesterday.
– Brain Games text p. 129 & 137
Copy HW in your planner.
– Text p. 141, #12-38 even
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. 129 Brain Game
Patent Puzzle - 1873
Homework
Text p. 137 Brain Game
All Boxed In – 7 small
boxes; 45 small boxes; 7
large boxes
Objective
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SWBAT solve simple inequalities and
use inequalities to solve real-life
problems
Section 3.4, “ Solving 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
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
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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.
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.
Homework
Text p. 141, #12-38 even