3-5 Inequalities
Preview
Evaluating Algebraic Expressions
Warm Up
California Standards
Lesson Presentation
3-5 Inequalities
Warm Up
Order each set of integers from least to
Evaluating Algebraic Expressions
greatest.
1. –7, 8, –9
–9, –7, 8
2. –2, 2, 0, -1
–2, –1, 0, 2
3. –11, -13, -10 –13, –11, –10
Write an algebraic expression for each word
phrase.
4. 2 less than g g – 2
5. 5 minus the product of 3 and m 5 – 3m
6. 1 more than the quotient of x and 4 1 + x
4
3-5 Inequalities
Evaluating
Algebraic Expressions
California
Standards
AF1.1 Use variables and appropriate
operators to write an expression, an equation, an
inequality, or a system of equations or inequalities
that represents a verbal description (e.g., three
less than a number, half as large as area A).
3-5 Inequalities
Vocabulary
Evaluating
Algebraic Expressions
inequality
algebraic inequality
solution set
3-5 Inequalities
An inequality compares two expressions using <,
>, , or .
Evaluating Algebraic Expressions
Symbol
<
>
Meaning
Word Phrases
is less than
Fewer than, below
More than, above
≤
is greater than
is less than or
equal to
≥
is greater than
or equal to
At least, no less than
At most, no more than
An inequality that contains a variable is an
algebraic inequality.
3-5 Inequalities
Additional Example 1: Translating Word Phrases
into Inequalities
Evaluating Algebraic Expressions
Write an inequality for each situation.
A. There are at least 35 people in the gym.
Let p = the number of people in the gym.
p ≥ 35 “At least” means greater than or equal to.
B. The carton holds at most 12 eggs.
Let e = the number of eggs the carton hold.
e ≤ 12 “At most” means less than or equal to.
3-5 Inequalities
Check It Out! Example 1
Evaluating
Algebraic
Expressions
Write
an inequality
for each situation.
A. There are at most 10 gallons of gas in the tank.
Let g = the number of gallons of gas.
g ≤ 10 “At most” means less than or equal to.
B. There are fewer than 10 yards of fabric left.
Let y = the yards of fabric.
y < 10
“Fewer than” means less than.
3-5 Inequalities
Additional Example 2: Writing Inequalities
Write
an inequality
for each statement.
Evaluating
Algebraic
Expressions
A. A number m multiplied by 5 is less than 25.
A number m multiplied by 5 is less than 25.
m

5
<
25
5m < 25
B. The sum of a number y and 16 is no more
than 100.
The sum of a number y and 16 is no more than 100
y + 16
≤
100
y + 16 ≤ 100
3-5 Inequalities
Check It Out! Example 2
Write an inequality for each statement.
Evaluating Algebraic Expressions
A. A number y plus 14 is greater than 21.
A number y plus
14 is greater than 21.
y
+
14
>
21
y + 14 > 21
B. A number t increased by 7 is more than 11
A number t
t
is increased by
7
+
7
t + 7 > 11
is more than
11
>
11
3-5 Inequalities
Algebraic
A Evaluating
solution of an inequality
is any Expressions
value of the
variable that makes the inequality true. All of the
solutions of an inequality are called the solution
set.
You can graph the solution set on a number line.
The symbols < and > indicate an open circle.
3-5 Inequalities
This open circle shows that 5 is not a solution.
Evaluating Algebraic Expressions
a>5
The symbols ≤ and ≥ indicate a closed circle.
This closed circle shows that 3 is a solution.
b≤3
3-5 Inequalities
Additional Example 3: Graphing Inequalities
Evaluating Algebraic Expressions
Graph each inequality.
A. –1 > y
–3
–2
–1
0
1
2
3
B. z ≥ –2 1
2
–3
–2
–1
0
1
2
3
Draw an open circle at
–1. The solutions are
all values of y less
than –1, so shade the
line to the left of –1.
Draw a closed circle
1
at –2 2 and all values of z
1
greater than -2 2. So
shade to the right of –2 1 .
2
3-5 Inequalities
Check It Out! Example 3
Graph
each inequality.
Evaluating
Algebraic
A. n < 3
–3
–2
–1
0
1
2
3
B. a ≥ –4
–6
–4
–2
0
2
4
6
Expressions
Draw an open circle at
3. The solutions are all
values of n less than 3,
so shade the line to the
left of 3.
Draw a closed circle
at –4. The solutions are
all values greater than
–4, so shade to the right
of –4.
3-5 Inequalities
Evaluating Algebraic Expressions
A compound inequality is the result of
combining two inequalities. The words and and
or are used to describe how the two parts are
related.
Writing Math
The compound inequality –2 < y and y < 4
can be written as –2 < y < 4.
3-5 Inequalities
Additional Example 4: Writing Compound
Inequalities
Algebraic
WriteEvaluating
a compound inequality
for Expressions
each statement.
A. A number x is both less than 4 and greater
than or equal to –2.5.
–2.5 ≤ x < 4
B. A number t is either greater than –1 or less
than or equal to –7.
t > –1 or t ≤ –7
3-5 Inequalities
Check It Out! Example 4
Write a compound inequality for each statement.
Evaluating Algebraic Expressions
A. A number t is both greater than 9 and less
than or equal to 18.5
9 < t  18.5
B. A number y is either greater than –5 or less
than or equal to –1.
y > –5 or y ≤ –1
3-5 Inequalities
Lesson Quiz: Part I
Write an inequality for each situation.
Evaluating Algebraic Expressions
1. Fewer than 150 people bought tickets.
p < 150
2. There are at least 20 finches in the cage.
f ≥ 20
Write an inequality for each statement.
3. A number n decreased by 5 is at most 16.
n – 5 ≤ 16
4. The product of 15 and a number z is greater than
100. 15z > 100
3-5 Inequalities
Lesson Quiz: Part II
Graph each inequality.
Evaluating Algebraic Expressions
5. m ≤ 1
–3 –2 –1
0
1 2
3
–2 –1 0
1 2
3
6. –3 < y
º
–3