Title: Warm Up
1Warm Up
Problem of the Day
Lesson Presentation
2Warm Up Compare. Use gt, lt, or .
gt
gt
1. 3 4
2. 6 2
lt
3. 8 5
4. 5 5
gt
lt
5. 3 3
6. 8 2
3Problem of the Day Elliot led the race Gordon
was ahead of Wallace. Labonte was directly behind
Gordon and directly ahead of Marlin. Who was in
last place ?
Wallace
4Learn to solve inequalities with integers.
5When you pour salt on ice, the ice begins to
melt. If enough salt is added, the resulting
saltwater will have a freezing point of 21C,
which is much less than waters freezing point of
0C.
Adding rock salt to the ice lowers the freezing
point and helps to freeze the ice cream mixture.
At its freezing point, a substance begins to
freeze. To stay frozen, the substance must
maintain a temperature that is less than or equal
to its freezing point.
6If you add salt to the ice that is at a
temperature of 4C, what must the temperature
change be to keep the ice from melting?
This problem can be expressed as the following
inequality 4 t ? 21
When you add 4 to both sides and solve, you find
that if t ? 17, the ice will remain frozen.
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8Additional Example 1A Adding and Subtracting to
Solve Inequalities
Solve and graph.
A. k 3 gt 2
Subtract 3 from both sides.
k gt 5
5
0
9Additional Example 1B Adding and Subtracting to
Solve Inequalities Continued
Solve and graph.
B. r 9 ? 12
r 9 ? 12
r 9 9 ? 12 9
Add 9 to both sides.
r ? 21
21
15
24
10Additional Example 1C Adding and Subtracting to
Solve Inequalities Continued
Solve and graph.
C. u 5 ? 3
u 5 ? 3
Add 5 to both sides.
u 5 5 ? 3 5
u ? 8
8
5
0
10
11Additional Example 1D Adding and Subtracting to
Solve Inequalities Continued
Solve and graph.
D. c 6 ? 2
c 6 ? 2
Subtract 6 from both sides.
c ? 4
7
0
4
4
12Try This Example 1A
Solve and graph.
A. y 7 ? 1
Subtract 7 from both sides.
y ? 8
13Try This Example 1B
Solve and graph.
B. f 4 ? 8
f 4 ? 8
f 4 4 ? 8 4
Add 4 to both sides.
r ? 12
14Try This Example 1C
Solve and graph.
C. r 2 lt 1
r 2 lt 1
r 2 2 lt 1 2
Add 2 to both sides.
r lt 3
15Try This Example 1D
Solve and graph.
D. d 9 ? 6
d 9 ? 6
Subtract 9 from both sides.
d ? 3
16Sometimes you must multiply or divide to isolate
the variable. Multiplying or dividing both sides
of an inequality by a negative number gives a
surprising result.
5 gt 1
5 is greater than 1.
1 5 1 (1)
Multiply both sides by 1.
5 1
gt or lt ?
5 lt 1
You know 5 is less than 1, so you should use lt.
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19Additional Example 2 Multiplying and Dividing to
Solve Inequalities
Solve and graph.
A. 3y ? 15
Divide each side by 3 ? changes to ?.
y ? 5
B. 7m lt 21
Divide each side by 7.
m lt 3
20Try This Example 2
Solve and graph.
A. 8y ? 24
Divide each side by 8 changes gt to lt.
y ? 3
B. 9f gt 45
Divide each side by 9.
f gt 5
21Lesson Quiz Part 1
Solve and graph.
1. h 2 lt 0
h ? 2
2. c 5 gt 2
c ? 3
3. lt 1
t gt 3
7n gt 28
4.
n gt 4
22Lesson Quiz Part 2
A local weather forecast stated that it would be
12F tonight and at least 10 colder the next
night. Write an inequality to show how cold it
will be?
5.
x ? 2F