1. Solving & Graphing Inequalities
PS 4: Solve one- and two-step linear inequalities and graph the solutions on the number line.
LT 3: Solve two inequalities.
Materials Needed
Individual Interactive Notebooks
Pencil
Answer Sheet

2. You learned that an INEQUALITY compares using symbols:
Write this expression in words
>
(6)(7) (9)(5)
66 ÷ (8)(4)
– 3 – – 3 + 7
Comparison Practice

3. Algebraic Inequalities
You learned that ALBEBRAIC INEQUALITIES contain Variables:
b > ½
x ≥ 7
Write Three of Your Own
Algebraic Inequalities
k ≤ 100
5.9 < m
f ≤ 13

4. A SOLUTION makes the inequality TRUE.
(5)(3) 14 ?
The Inequality 15 14
<
The solution
Solve
Problem
Written with Solution Circled
1) ● 2
2) 54 ÷
3) (16)(3)

5. A SOLUTIONS SET is a RANGE of possible answers
“It anywhere from ____ to ____.
Fill in the empty boxes
Inequality
In Words
What are 3 possible solutions? Why?
1) x < 5
‘x’ is less than 5
32, -7, 3
they are all less than 5
2) a ≤ -3
3) y > 11

6. How to write answers for a SOLUTION SET?
Arrows & Points
How to write answers for a SOLUTION SET?
For ‘less than’, the arrow points down
When there is not an equals line, the point is open.
f < 2
For ‘more than’, the arrow points up
When there is an equals line, the point is closed.
f ≥ 2

7. Graph the solution set for each inequality.
Practice
Which direction does the arrow go?
2) Is the point open or closed?
Remember!
Graph the solution set for each inequality.
Inequality
Solution Set
x ≤ -1
h > 10
w < -7

8. One-Step Inequalities

9. Solving for Inequalities is EXACTLY like EQUATIONS.
YOU KNOW THIS SIDE!
Solution Set
x + 7 = 10
x + 7 ≤ 10
- 7 = - 7
- 7 ≤ - 7
x = 3
x ≤ 3
Subtract 7
From both
Sides.
Bring down
what’s left.
Equals line
closed point
Q: Why don’t we graph the equation?
A: We know the answer, it’s 4.
Q: Why do we graph the inequality?
A: To show all possible answers. We’re not sure exactly, but we know it’s 3 or lower.

10. a + 6 ≥ 8 24 ≤ 6w ─ 6 a ≥ ≤ w Example 1 Example 2
1. To solve, fill in the boxes above.
2. Insert an arrow going in the correct direction below.
1. To solve, fill in the boxes above.
2. Insert the appropriate open or closed point below.

11. w k ─ 2 < 3 > -1 4 k < ) ( ) ( > Example 3 Example 4
1. To solve, fill in the boxes above.
2. Write the SOLUTION SET FOR example 4 below.
1. To solve, fill in the boxes above.
2. Insert an arrow going in the correct direction below.

12. Practice x + 6 > 15 2. y + 8 < 8 3. 5z ≤ 35 4. a – 7 ≥ 13 b 6
Inequality
Solution Set
x + 6 > 15
2. y + 8 < 8
3. 5z ≤ 35
4. a – 7 ≥ 13 b 6
> 3

13. Two-Step Inequalities

14. Solving for 2 step Inequalities is EXACTLY like EQUATIONS.
YOU KNOW THIS SIDE!
Solution Set
5x + 8 = 18
5x + 8 ≤ 18
- 8 = - 8
- 8 ≤ - 8
5x = 10
5x ≤ 10
x = 2
x ≤ 2
Subtract 8
From both
Sides.
Divide by 5
on both Sides.
Q: Why don’t we graph the equation?
A: We know the answer, it’s 2.
Q: Why do we graph the inequality?
A: To show all possible answers. We’re not sure exactly, but we know it’s 2 or lower.

15. 5a ─ 5 > 10 18 < 6w + 6 5a < 6w < w + 5 > a >
Example 1
Example 2
5a ─ 5 > 10
18 < 6w + 6
+ 5 5a
>
< 6w a
>
< w
Insert an arrow going in the correct direction below.
Insert the appropriate open or closed point below.

16. w 2k + 12 ≤ 12 4 + 5 ≥ 8 ≤ k w ≥ Example 3 Example 4
Write the SOLUTION SET FOR examples 3 and 4 below.

17. Practice 3x + 14 > 38 2. 5y – 5 < 55 3. 3z – 15 ≤ 15
Inequality
Solution Set
3x + 14 > 38
2. 5y – 5 < 55
3. 3z – 15 ≤ 15
4. 3a – 3 ≥ 0 b 2
+ 6 > 6