1. 2-5 Lesson Presentation Solving Inequalities Containing Integers
Course 3
Lesson Presentation

2. 2-5 Learn to solve inequalities with integers.
Course 3
2-5
Solving Inequalities Containing Integers
Learn to solve inequalities with integers.

3. 2-5 Solving Inequalities Containing Integers
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.
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.

4. 2-5 Solving Inequalities Containing Integers
Course 3
2-5
Solving Inequalities Containing Integers
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?
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.

5. 2-5 Solving Inequalities Containing Integers
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!

6. Additional Example 1A: Adding and Subtracting to Solve Inequalities
Course 3
2-5
Solving Inequalities Containing Integers
Additional Example 1A: Adding and Subtracting to Solve Inequalities
Solve and graph.
A. k +3 > –2 –3
k +3 > –2
Subtract 3 from both sides.
k > –5 –5

7. 2-5 Solving Inequalities Containing Integers Solve and graph.
Course 3
2-5
Solving Inequalities Containing Integers
Additional Example 1B: Adding and Subtracting to Solve Inequalities Continued
Solve and graph.
B. r – 9  12
r – 9  12
r – 
Add 9 to both sides.
r  21 15 21 24

8. Solving inequalities is almost identical to solving equations :
Even Better News !
Solving inequalities is almost identical to solving equations :
Example 1
x is any value less than 4
28-Mar-17

9. Solving inequalities is almost identical to solving equations :
Example 2
x is any value greater than or equal to 5
28-Mar-17

10. 2-5 Solving Inequalities Containing Integers 5 > –1
Course 3
2-5
Solving Inequalities Containing Integers
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
5 is greater than –1.
–1 • 5 –1 • (–1)
Multiply both sides by –1. –
> or < ?
–5 < 1
You know –5 is less than 1, so you should use <.
–5 < 1
–7 –6 –5 –4 –3 –2 –
5 > –1

11. MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS
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.

12. 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

13. Additional Example 2: Multiplying and Dividing to Solve Inequalities
Course 3
2-5
Solving Inequalities Containing Integers
Additional Example 2: Multiplying and Dividing to Solve Inequalities
Solve and graph.
A. –3y  15
Divide each side by –3;  changes to .
–3y  15 –3 –7 –5 4
y  –5
B. 7m < 21
7m < 21 7
Divide each side by 7. 3 –3 5
m < 3

14. > Solving Inequalities 8 – 3m < 2 -3m < -6 -3 So m > 2
The only one to watch out for is when you are dividing by a negative
Example
8 – 3m < 2
-3m < -6
Subtract 8 from each side
m -6 -3
>
Divide across by -3 and change the Sign
So m > 2
28-Mar-17

15. ≤ Solving Inequalities 5( x – 1 ) - 8x ≥ - 17 5x – 5 – 8x ≥ - 17
Example 2
5( x – 1 ) - 8x ≥ - 17
5x – 5 – 8x ≥ - 17
- 3x - 5 ≥ - 17
- 3x ≥ - 12 x -3 ≤
So x ≤ 4
28-Mar-17

16. 2-5 –2 –3 –3 Solving Inequalities Containing Integers Solve and graph.
Course 3
2-5
Solving Inequalities Containing Integers
Lesson Quiz: Part 1
Solve and graph.
1. h + 2 < 0 –2 2
h  –2
2. c – 5 > –2 3 –3
c  3 t –3
< 1 3 –3
t > –3 4.
7n > 28 4 8
n > 4

17. 2-5 5. x  2°F Solving Inequalities Containing Integers
Course 3
2-5
Solving Inequalities Containing Integers
Lesson Quiz: Part 2 5.
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?
x  2°F