Transcript Do Now 12/8/06

Do Now 11/12/09
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Take out HW from last night.
– Text p. 141, #12-38 evens
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Copy HW in your planner.
– Text p. 146, #12-36 evens
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In your journal, describe the process (steps
that you take) in order to solve and graph an
inequality. Then solve and graph the following
two inequalities.
x  8  4
x 18  74
Homework
Text p. 141, #12-38 evens
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w ≤ 2500
w ≤ 7700
s ≤ 50
x ≥ -5
x < -20
m≥4
-1 ≥ d or d ≤ -1
z > 87
h ≤ -4
t < 10.4
a > 15.5
m≥1
p > 32
t ≥ -280
Solve x – 5 > -3.5
Graph your solution
x – 5 > – 3.5
+ 5 + 5.0
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 9 ≥ x + 7
Graph your solution
9≥x+7
–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.
Section 3.5
“Solve Inequalities Using Multiplication and
Division”
INEQUALITIES –
mathematical sentence formed by
placing a <, ≤, >, or ≥ between
two expressions.
3y < 12
r ÷ 4 > 30
(a/11) ≤ 121
120 ≥ 4z
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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 < 3
-4
-3
-2
-1
“Less than or equal to”
and “greater than or equal
to” are represented with
closed circle.
-4
-3
-2
0
1
2
3
4
5
6
Graph x ≥ -1
-1
0
1
2
3
4
5
6
x
Solve  5 . Graph your solution.
4
x
< 5.
4
4 x <4 5
4
x < 20
Write original inequality.
Multiply each side by 4.
Simplify.
ANSWER
The solutions are all real numbers
less than 20. Check by substituting
a number less than 20 in the
original inequality.
m
Solve  2. Graph your solution.
8
8
m
≤–2
8
m
≤–2 8
8
m ≤ – 16
Write original inequality.
Multiply each side by 8.
Simplify.
The solutions are all real numbers less than are
equal to – 16. Check by substituting a number
less than – 16 in the original inequality.
Solve Inequalities When Multiplying and
Dividing by a NEGATIVE”
Multiplying and/or dividing each side
of an inequality by a NEGATIVE number
only produces an equivalent inequality
IF the inequality sign is REVERSED!!
m
 1.6 . Graph your solution.
Solve
7
m
– 7 < 1.6
m
– 7 – 7 > – 7 1.6
m > – 11.2
Write original inequality.
Multiply each side by – 7.
Reverse inequality symbol.
Simplify.
ANSWER
The solutions are all real numbers greater than – 11.2.
Check by substituting a number greater than – 11.2 in the
original inequality.
Solve  3x .24
–3x > 24.
–3x
< 24
–3
–3
x<–8
Write original inequality.
Divide each side by –3. Reverse
inequality symbol.
Simplify.
Solve a real-world problem
A student pilot plans to spend 80 hours on flight training to
earn a private license. The student has saved $6000 for training.
Which inequality can you use to find the possible hourly rates r
that the student can afford to pay for training?
A 80r < 6000 B 80r <
– 6000 C 80r >
– 6000 D 80r > 6000
SOLUTION
The total cost of training can be at most the amount of money
that the student has saved. Write a verbal model for the
situation. Then write an inequality.
80
r
The correct answer is B. A
<
–
B
6000
C
D
Solve a real-world problem
What are the possible
hourly rates that the
student can afford to pay
for training?
80
r ≤ 6000
80r ≤ 6000
80
80
r ≤ 75
Write inequality.
Divide each side by 80.
Simplify.
The student can afford to pay at most $75 per hour
for training.
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Homework
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Text p. 146, #12-36 evens