3-1 Graphing and Writing Inequalities
Objectives
Identify solutions of inequalities with one
variable.
Write and graph inequalities with one variable.
Holt Algebra 1
3-1 Graphing and Writing Inequalities
An inequality is a statement that two quantities
are not equal. The quantities are compared by
using the following signs:
≥
≠
A≤B
A≥B
A≠B
A is less
than or
equal to B.
A is greater
than or
equal to B.
A is not
equal to B.
<
>
≤
A<B
A>B
A is less
than B.
A is greater
than B.
A solution of an inequality is any value that
makes the inequality true.
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Do not copy!
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Example 1:
Graph each inequality.
A. m ≥
–
0
1
2
3
3
8
10 12
B. t < 5(–1 + 3)
t < 5(–1 + 3)
t < 5(2)
t < 10
–8 –6 –4 –2 0
Holt Algebra 1
2
4
6
3-1 Graphing and Writing Inequalities
Example 2
Graph each inequality.
a. c > 2.5
2.5
–4 –3 –2 –1
0
1
2
3
4
5
6
2
3
4
5
6
b. 22 – 4 ≥ w
22 – 4 ≥ w
4–4≥
w 0≥w
–4 –3 –2 –1 0
Holt Algebra 1
1
3-1 Graphing and Writing Inequalities
Example 3: Writing an Inequality from a Graph
Write the inequality shown by each graph.
x<2
x ≥ –0.5
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Reading Math
“No more than” means “less than or
equal to.”
“At least” means “greater than or
equal to”.
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Check It Out! Example 4
A store’s employees earn at least $8.50 per
hour. Define a variable and write an
inequality for the amount the employees
may earn per hour. Graph the solutions.
Let w represent an employee’s
An employee earns
at least
w
≥
w ≥ 8.5
−2 0
Holt Algebra 1
Define a variable
means write a let
wages.
statement
2 4
8.5
6
8 10 12 14 16 18
$8.50
8.50
3-1 Graphing and Writing Inequalities
Lesson Quiz: Part I
1. Describe the solutions of 7 < x + 4.
all real numbers greater than 3
2. Graph h ≥ –4.75
–5
–4.75
–4.5
Write the inequality shown by each graph.
3.
4.
Holt Algebra 1
x≥3
x < –5.5