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Use interval notation to indicate the graphed
numbers.
(-2, 3]
(-, 1]
2-8: Solving Absolute-Value
Equations and Inequalities
Part 1: Solving Compound Inequalities Disjunctions
Compound inequality – 2 or more
inequalities
Disjunction - compound inequality
that uses the word or. Has 2 separate
pieces.
Identifying Disjunctions
*3 Categories*
Category
Inequalities
Description
The word “OR” is between 2 inequalities
x ≤ –3 OR x > 2
Number line graph
Two separate graphs
Set-builder Notation
2 inequalities are separated by the symbol U (union)
Set builder notation: {x|x ≤ –3 U x > 2}
Identifying Disjunctions
*Determine whether the example is a disjunction or
not a disjunction*
6y < –24 OR y +5 ≥ 3
x ≥ –3 AND x < 2
x – 5 < –2 OR –2x ≤ –10
Identifying Disjunctions
*Determine whether the example is a disjunction or
not a disjunction*
–3 –2 –1
0
1
2
3
4
5
6
–6 –5 –4 –3 –2 –1
0
1
2
3
–6 –5 –4 –3 –2 –1
0
1
2
3
Identifying Disjunctions
*Determine whether the example is a disjunction or
not a disjunction*
Solving & Graphing Disjunctions
Step 1
Step 2
Step 3
Step 4
Solve each inequality for the
variable.
Graph both solutions on the number
line.
Write you answer in set-builder
notation.
Write you answer in interval notation.
Example 1
Solve the compound inequality. Then graph the solution set.
6y < –24 OR y +5 ≥ 3
Solve both inequalities for y.
or
6y < –24
y + 5 ≥3
y < –4
y ≥ –2
The solution set is all points that satisfy
{y|y < –4 U y ≥ –2}.
–6 –5 –4 –3 –2 –1
0
1
2
3
(–∞, –4) U [–2, ∞)
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<3
x≥5
The solution set is the set of all points that satisfy
{x|x < 3 U x ≥ 5}.
–3 –2 –1
0
1
2
3
4
5
6
(–∞, 3) U [5, ∞)
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
x≥6
or
x<3
The solution set is all points that satisfy
{x|x < 3 U x ≥ 6}.
–1
0
1
2
3
4
5
6
7
8
(–∞, 3) U [6, ∞)
Example 4
Solve the compound inequality. Then graph the solution set.
x –5 < 12 OR 6x ≤ 12
Solve both inequalities for x.
x –5 < 12
or
6x ≤ 12
x≤2
x < 17
Because every point that satisfies x < 2 also satisfies x < 2, the
solution set is {x|x < 17}.
(-∞, 17)
2
4
6
8
10 12 14 16 18 20
In tribes complete the worksheet!
For each question:
1. Solve
2. Graph
3. Write in set-builder
4. Write in interval
Exit Slip: Define disjunction. Give me an example of a
disjunction and an example of something that is not a
disjunction.