Algebra 2
Chapter 1 Section 6
Objectives:
1. Solve compound inequalities
2. Solve absolute value inequalities
Standards:
A2.2.1c, A2.2.1d, and SMP 1,2,5,7,8
Compound Inequalities

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Compound Inequality – a pair of inequalities joined
by “and” or “or”
Ex: -1 < x and x ≤ 3 which can be written as
-1 < x ≤ 3 because the variable is between -1
and 3
x < -1 or x ≥ 3
For “and” statements the value must satisfy both
inequalities
For “or” statements the value must satisfy one of the
inequalities
And Inequalities
a)
Graph the solution of
3x – 1 > -28 and 2x + 7 < 19.
3x > -27 and 2x < 12
x > -9 and x < 6
b)
Graph the solution of -8 < 3x + 1 <19
-9 < 3x < 18
-3 < x < 6
Or Inequalities
ALGEBRA 2 LESSON 1-4
Graph the solution of 3x + 9 < –3 or –2x + 1 < 5.
3x + 9 < –3
or
–2x + 1 < 5
3x < –12
–2x < 4
x < –4 or x > –2
Try These Problems
Graph the solution of 2x > x + 6 and x – 7 < 2
a)
a)
x > 6 and x < 9
Graph the solution of x – 1 < 3 or x + 3 > 8
b)
a)
x < 4 or x > 11
Absolute Value Inequalities
Let k represent a positive real number
 │x │ ≥ k is equivalent to x ≤ -k or x ≥ k
 Same work as an “or” inequality
 │x │ ≤ k
is equivalent to
-k ≤ x ≤ k
 Same work as an “and” inequality
 Remember to isolate the absolute value
before rewriting the problem with two
inequalities
Solve |2x – 5| > 3. Graph the solution. (This
is the same as doing an “or” compound inequality.)
|2x – 5| > 3
2x – 5 < –3 or 2x – 5 > 3
2x < 2
2x > 8
x < 1 or
x>4
Rewrite as a compound inequality.
Solve for x.
Try This Problem
Solve │2x - 3 │ > 7
2x – 3 > 7
2x > 10
x>5
or
or
or
2x – 3 < -7
2x < -4
x < -2
Solve –2|x + 1| + 5
>
– –3.
Graph the solution.
–2|x + 1| + 5 >
– –3
–2|x + 1| >
– –8
|x + 1| <
–4
Isolate the absolute value expression.
Subtract 5 from each side.
Divide each side by –2 and reverse
the inequality.
–4 <
– x + 1<
–4
Rewrite as a compound inequality.
–5 <
–x<
–3
Solve for x.
Try This Problem
Solve |5z + 3| - 7 < 34. Graph the solution. (This
is the same as an “and” inequality.)
|5z + 3| -7 < 34
|5z + 3| < 41
-41 < 5z + 3 < 41
-44 < 5z < 38
-44/ <
38/
z
<
5
5
-8 4/5 < z < 7 3/5
Ranges in Measurement
 Absolute value inequalities and
compound inequalities can be used to
specify an allowable range in
measurement.
Margin of Error

The area A in square inches of a square photo is required to
satisfy 8.5 ≤ A ≤ 8.9. Write this requirement as an absolute
value inequality.
8.9 – 8.5
0.4
=
2
2 = 0.2
8.9 + 8.5
17.4
=
2
2 = 8.7
Find the difference margin for the area boundaries.
Find the average of the maximum and
minimum values.
–0.2 <
– A – 8.7 <
– 0.2
Write an inequality.
|A – 8.7| <
– 0.2
Rewrite as an absolute value inequality.
Try This Problem
The specification for the circumference C in inches of a
basketball for junior high school is 27.75 ≤ C ≤ 30.
Write the specification as an absolute value inequality.
28.5  27.75 .75

 .375
2
2
Find the difference
margin.
28.5  27.75 56.25

 28.125
2
2
C  28.125  .375
Find the average from min and
max values.
Write the absolute value inequality.
Homework
 Practice 1.6
 Pages 45-48 #13-51 odd