Download "Or" Type Compound Inequalities

6-4B Solving Compound
Inequalities Involving “OR”
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
A compound inequality consists of two inequalities
connected by the word “AND” or the word “OR”.
Compound inequalities involving
“AND” consist of two inequalities.
Both must be satisfied to make
the compound inequality true. The
solution of these two inequalities will
graph as a line segment.
If you want to go to the movies with your friends
you must finish your homework and clean your room.
You would need to satisfy both conditions before
you could go to the movies.
Compound inequalities involving “OR” consist of two
inequalities, either of which can be satisfied to make the
compound inequality true.
If you want to go to the movies with your friends you
must finish your homework or clean your room.
Lucky you! Only one condition needs to be satisfied
before you can go to the movies.
Write a compound inequality that represents the set of all
real numbers less than –3 or greater than 0. Then graph
the inequality.
0
n  –33 or n  0
O
O
Compound inequalities involving OR will graph as opposite
rays. Notice the inequality symbols are pointing away from
each other. There are infinite solutions!
Notes to
record!
O R
Opposite Rays
Compound inequalities with “OR” are written as
two inequalities – the word “or” is mandatory.
n  3 or
n 0
Write in
your notes
and
highlight!
Write a compound inequality that represents the set of all
real numbers greater than 0 or less than –3. Then graph
the inequality.
or
n0
or nn  3
Reposition the
inequalities to
0
–3
reflect the
Whoa – these signs
O
O
are pointing
towards
endpoints order
one another. This
on a number line.
Write the
above note
in your
spiral.
compound inequality
is not written in
good form!
Example 1 Soup Plantation offers a reduced price for
children less than or equal to 12 years of age or for adults
over age 65. Write a compound inequality to describe the
age of those people who can eat for a reduced price. Then
graph the inequality.
1. Write the two inequalities.
2. Graph.
a  12
•
12
or
a  65
O
65
Solving Compound Inequalities with “OR”.
Write both inequalities.
Solve each inequality
independently.
Write “or” between
the inequalities.
x4  3
4 4
x  7
•
or
2x  18
2
2
x  9
O
Compound inequalities involving OR will graph as opposite
rays. Notice the inequality symbols are pointing away from
each other. There are infinite solutions!
More notes
to record!
Solve. Then graph the solution.
Example 2 x  5   6
or
3x  12
Example 3 8x  1  25 or 6x  5  7
Example 4  32y  64  32 or  32y  64   32
Example 2 Solve the inequality. Then graph the solution.
x5  6
5
5
x   11
O
–11
or
or
3x  12
3
3
•
4
x4
Example 3 Solve the inequality. Then graph the solution.
Reposition the
inequalities to
reflect the
endpoints order
on a number line.
8x  1  25 or 6x  5  7
1
1
5 5
6x  12
8x  24
6
6
8
8
x  2
x
x 3
or
O
2
O
3
Example 4 Solve the inequality. Then graph the solution.
 32y  64  32 or  32y  64   32



64
 64
 64 64
Reverse sign
 32y /  32
 32y /  96
when multiplying
 32 <  32
 32 >  32
by a negative.
y 3
or
y  1
O
O
1
3
Solve.
Example 5
3x  5   19
Example 6
 8x  24 or 2x  5  1 7
Example 7
1  5y  14 or  3y  2  7
Example 8
3x  8  17 or 2x  5  7
Example 9
6  2x  20 or 8  x  0
or
4x  7   1
Write an inequality and then solve.
Example 10 The product of -5 and a number is
greater than 35 or less than 10.
Example 5 Solve.
Example 6 Solve.
3x  5   19 or
5 5
3x   24
3
3
x  8
 8x 
/ 24
 8 < 8
x  3
or
4x  7   1
7 7
4x   8
4
4
x  2
2x  5  17
5 5
2x  22
2
2
x  11
Example 7 Solve.
Reposition the
inequalities to
reflect the
endpoints order
on a number line.
Example 8 Solve.
1  5y  14 or  3y  2  7
1
1
2 2
 5y 
/  15
 3y  9
>
5
5
3 3
y 3
yy  33
3x  8  17 or
or 2x  5  7
5 5
8 8
2x  2
3x  9
2
2
3
3
x3
xx 11
Example 9 Solve.
Reposition the
inequalities to
reflect the
endpoints order
on a number line.
6  2x  20 or
or 8  x  0
6
6
8
8
2x  14
x
x  88
2
2
xx  77
Example 10 The product of -5 and a number is greater
than 35 or less than 10.
 5n / 35 or  5n / 10
5 < 5
 5 > 5
n  2
n  7
The graph of the solution to a
compound inequality involving “AND”
is a line segment.
The graph of the solution to a
compound inequality involving “OR” is
two rays going in opposite direction
(opposite rays).
6-A9 Pages 318-319 # 13–16, 18, 19, 21, 22,
26–32, 34, 35, 38-41.