Starter:
Renaissance is having a winter carnival!
Admission into the carnival is $3 and each
game inside the carnival costs $0.25.
1)Write an inequality that represents the
possible number of games that can be played
having $10.
2) What is the maximum number of games that
can be played?
Solving Compound
Inequalities
6.3
Essential Questions
How does a Compound Inequality
differ from a regular inequality?
What is the meaning of “AND” and
“OR” in a Compound Inequality?
Do I still flip my sign in certain cases
with a Compound Inequality?
What is a Compound
Inequality?
A Compound Inequality
consists of two inequalities
that are joined by “AND” or
“OR”
What’s the difference
between “AND” and “OR”?
“AND” means
intersection. What do the
two items have in
common?
“OR” means union,
if it is in one item,
it is in the solution.
“AND” vs. “OR”
“AND” indicates that both
statements of the compound
inequality must be true at the same
time
“OR” indicates that as long as either
statement is true, then the entire
compound inequality is true
Write an inequality that represents
the set of numbers and sketch its
graph.
All real numbers that are greater
than or equal to -2 and less than
3.
-2 ≤ x < 3
-2 ≤ x and x < 3
-5 -4 -3 -2 -1
0
1
2
3
4
5
Write an inequality that represents
the set of numbers and sketch its
graph.
All real numbers that are greater
than -4 and less than or equal to
2.
-4 < x ≤ 2
-4 < x and x ≤ 2
-5 -4 -3 -2 -1
0
1
2
3
4
5
You Try!
All real numbers that are greater
than or equal to -3 and less than
0.
-3 ≤ x < 0
-3 ≤ x and x < 0
-5 -4 -3 -2 -1
0
1
2
3
4
5
Write an inequality that represents
the set of numbers and sketch its
graph.
All real numbers that are less
than or equal to -2 or greater than
3.
x ≤ -2 or x > 3
-5 -4 -3 -2 -1
0
1
2
3
4
5
Write an inequality that represents
the set of numbers and sketch its
graph.
All real numbers that are less
than -1 or greater than 1.
x < -1 or x > 1
-5 -4 -3 -2 -1
0
1
2
3
4
5
Your Turn!
All real numbers that are less
than or equal to -3 or greater than
0.
x ≤ -3 or x > 0
-5 -4 -3 -2 -1
0
1
2
3
4
5
Solving a Compound
Inequality with “AND”
-15 ˂ 9x + 3 ≤ 12
Solve the Inequality:
–8 ˂ x – 2 ≤ 7
Your Turn!
Solve the Inequality:
1) –5 ≤ 2x + 3 ˂ 7
–4 ≤ x ˂ 2
2) 4 ≥ 3x + 1 > -2
1 ≥ x > -1
or –1 ˂ x ≤ 1
Reversing both
Inequality Symbols:
-14 ≤ –3x – 2 ≤ 13
Your Turn!
Solve the Inequality:
1) –3 < -1 - 2x ≤ 5
1 > x ≥ -3
or –3 ≤ x ˂ 1
2) -1 ≥ -5x + 4 > 19
1≤x˂3
Solving a Compound
Inequality with “OR”
2x + 7 ˂ -11 or -3x - 2 < 13
Your Turn!
Solve the Inequality:
1) –6x + 9 < 3 or -3x - 8 > 13
x > 1 or x < 7
2) 6x - 5 < 7 or 8x + 1 > 25
x < 2 or x > 3
3) -3x + 5 > 8 or -x < -4
x < -1 or x > 4
Real Life
Write a Compound
Inequality:
Water is a non-liquid when the
temperature is 32°F or below, or is at
least 212°F
T ≤ 32 or T ≥ 212
A refrigerator is designed to work on
an electric line carrying from 115 volts
to 120 volts.
115 ≤ V ≤ 120
Wrapping Up
How does a Compound Inequality
differ from a regular inequality?
What is the meaning of “AND” and
“OR” in a Compound Inequality?
Do situations exist where the
inequality symbol in a Compound
Inequality must be reversed?