1. Use interval notation to indicate the graphed numbers.
Warm-Up
Use interval notation to indicate the graphed numbers.
(-2, 3]
(-, 1]

2. 2-8: Solving Absolute-Value Equations and Inequalities
Warning: Take noTes
On the sheet provided.
Completely fill-in and
Show To Ms. Lagroon at the
End of the period for full
class Work Credit 30%.
2-8: Solving Absolute-Value Equations and Inequalities
Part 1: Solving Compound Inequalities - Disjunctions

3. Compound inequality – 2 or more inequalities
Disjunction - compound inequality that uses the word or. Has 2 separate pieces.

4. Identifying Disjunctions
*3 Categories*
Category
Description
Inequalities
The word “OR” is between 2 inequalities
Number line graph
Two separate graphs
Set-builder Notation
2 inequalities are separated by the symbol U (union)
x ≤ –3 OR x > 2
Set builder notation: {x|x ≤ –3 U x > 2}

5. *Determine whether the example is a disjunction or not a disjunction*
Identifying Disjunctions
*Determine whether the example is a disjunction or not a disjunction*
6y < –24 OR y +5 ≥ 3
Disjunction
x ≥ –3 AND x < 2
Not a Disjunction
x – 5 < –2 OR –2x ≤ –10

6. *Determine whether the example is a disjunction or not a disjunction*
Identifying Disjunctions
*Determine whether the example is a disjunction or not a disjunction*
–3 –2 –
Disjunction
–6 –5 –4 –3 –2 –
Not a Disjunction
–6 –5 –4 –3 –2 –

7. *Determine whether the example is a disjunction or not a disjunction*
Identifying Disjunctions
*Determine whether the example is a disjunction or not a disjunction*

8. Solving & Graphing Disjunctions
Step 1
Solve each inequality for the variable.
Step 2
Graph both solutions on the number line.
Step 3
Write you answer in set-builder notation.
Step 4
Write you answer in interval notation.

9. Solve the compound inequality. Then graph the solution set.
Example 1
Solve the compound inequality. Then graph the solution set.
6y < –24 OR y +5 ≥ 3
Solve both inequalities for y.
6y < –24
y + 5 ≥3 or
y < –4
y ≥ –2
The solution set is all points that satisfy {y|y < –4 U y ≥ –2}.
–6 –5 –4 –3 –2 –
(–∞, –4) U [–2, ∞)

10. Solve the compound inequality. Then graph the solution set.
Example 2
Solve the compound inequality. Then graph the solution set.
x – 5 < –2 OR –2x ≤ –10
Solve both inequalities for x.
x – 5 < –2 or –2x ≤ –10
x < x ≥ 5
The solution set is the set of all points that satisfy {x|x < 3 U x ≥ 5}.
–3 –2 –
(–∞, 3) U [5, ∞)

11. Solve the compound inequality. Then graph the solution set.
Example 3
Solve the compound inequality. Then graph the solution set.
x – 2 < 1 OR 5x ≥ 30
Solve both inequalities for x.
x – 2 < 1
5x ≥ 30 or
x ≥ 6
x < 3
The solution set is all points that satisfy {x|x < 3 U x ≥ 6}. –
(–∞, 3) U [6, ∞)

12. Solve the compound inequality. Then graph the solution set.
Example 4
Solve the compound inequality. Then graph the solution set.
x –5 < 12 OR 6x ≤ 12
Solve both inequalities for x.
x –5 < or x ≤ 12
x < x ≤ 2
Because every point that satisfies x < 2 also satisfies x < 2, the solution set is {x|x < 17}.
(-∞, 17)

13. In tribes complete the worksheet!
For each question:
Solve
Graph
Write in set-builder
Write in interval
Exit Slip: Define disjunction. Give me an example of a disjunction and an example of something that is not a disjunction.