Learn to solve inequalities with integers'

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Learn to solve inequalities with integers.
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When 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.
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If 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 ? 21, the ice will remain frozen.
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Additional 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
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Additional 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
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Additional 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
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Additional 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
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Try This Example 1A
Solve and graph.
A. y 7 ? 1
Subtract 7 from both sides.
y ? 8
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Try 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
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Try 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
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Try This Example 1D
Solve and graph.
D. d 9 ? 6
d 9 ? 6
Subtract 9 from both sides.
d ? 3
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Sometimes 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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Additional 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
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Try 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
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Lesson 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
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Lesson 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