Download - 2-5 Solving Inequalities Containing Integers Course 3 Lesson Presentation Lesson Presentation
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2-5 Solving Inequalities Containing Integers
Course 3
Lesson Presentation
![Page 2: 2-5 Solving Inequalities Containing Integers Course 3 Lesson Presentation Lesson Presentation](https://reader036.vdocuments.mx/reader036/viewer/2022062511/551517aa550346a80c8b5e84/html5/thumbnails/2.jpg)
Learn to solve inequalities with integers.
Course 3
2-5 Solving Inequalities Containing Integers
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Course 3
2-5 Solving Inequalities Containing Integers
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 –21°C, which is much less than water’s freezing point of 0°C.
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.
Adding rock salt to the ice lowers the freezing point and helps to freeze the ice cream mixture.
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If you add salt to the ice that is at a temperature of –4°C, what must the temperature change be to keep the ice from melting?
Course 3
2-5 Solving Inequalities Containing Integers
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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Course 3
2-5 Solving Inequalities Containing Integers
The graph of an inequality shows all of the numbers that satisfy the inequality. When graphing inequalities on a number line, use solid circles ( ) for and and open circles ( ) for > and <.
Remember!
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Course 3
2-5 Solving Inequalities Containing Integers
k > –5
A. k +3 > –2
Subtract 3 from both sides.–3 –3
k +3 > –2
Solve and graph.
Additional Example 1A: Adding and Subtracting to Solve Inequalities
–5 0
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Course 3
2-5 Solving Inequalities Containing Integers
B. r – 9 12
r 21
Add 9 to both sides.r – 9 + 9 12 + 9r – 9 12
21 2415
Additional Example 1B: Adding and Subtracting to Solve Inequalities Continued
Solve and graph.
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10 Apr 202310 Apr 2023
Solving inequalities is almost identical to solving equations :
Solving Inequalities
2 1 7x 2 7 1x
Example 1
2 8x 4x x is any value less than 4
Even Better News !
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10 Apr 202310 Apr 2023
Solving inequalities is almost identical to solving equations :
Solving Inequalities
2(2 3) 9x x
4 6 9x x
Example 2
3 6 9x 3 15x
x is any value greater than or equal to 5
15 3x
5x
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–5 1
Course 3
2-5 Solving Inequalities Containing Integers
5 is greater than –1.
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 > –1 Multiply both sides by –1.–1 • 5 –1 • (–1) > or < ?
You know –5 is less than 1, so you should use <.
–5 < 1
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
–5 < 1
5 > –1
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Course 3
2-5 Solving Inequalities Containing Integers
3 > 1
–4 12
Multiply by –2
Divide by –4 1 –3
–6 < –2
MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS
Words Original Inequality
Multiply/Divide
Result
Multiplying or dividing by a negative number reverses the inequality symbol.
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Course 3
2-5 Solving Inequalities Containing Integers
The direction of the inequality changes only if the number you are using to multiply or divide by is negative.
Helpful Hint
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Course 3
2-5 Solving Inequalities Containing Integers
A. –3y 15
y –5
Divide each side by –3; changes to .
B. 7m < 21
m < 3
Divide each side by 7.
Additional Example 2: Multiplying and Dividing to Solve Inequalities
Solve and graph.
0 3–3 5
–3y 15–3 –3
7m < 21 7 7
–7 –5 0 4
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10 Apr 202310 Apr 2023
Solving Inequalities
The only one to watch out for is when you are dividing by a negative
Example
8 – 3m < 2
-3m < -6
m -6 -3
Subtract 8 from each side
Divide across by -3 and change the Sign
So m > 2
>
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10 Apr 202310 Apr 2023
Solving Inequalities
Example 2
5( x – 1 ) - 8x ≥ - 17
5x – 5 – 8x ≥ - 17
- 3x - 5 ≥ - 17
- 3x ≥ - 12
x -12 -3
≤ So x ≤ 4
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Course 3
2-5 Solving Inequalities Containing Integers
Lesson Quiz: Part 1Solve and graph.1. h + 2 < 0
2. c – 5 > –2
7n > 28
t
–33. < 1
h –2
n > 4
t > –3
c 3
–2 0 2
3–3 0
3–3 0
4 8 04.
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Course 3
2-5 Solving Inequalities Containing Integers
A local weather forecast stated that it would be 12°F tonight and at least 10° colder the next night. Write an inequality to show how cold it will be?
Lesson Quiz: Part 2
5.
x 2°F