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Section 3-1 Inequalities and their Graphs
SPI 22N: identify the graphical representation of the solution to a one
variable inequality on a number line
• Identify solutions of inequalities
• Graph and write inequalities
Solution of an inequality:
• any number that makes the equation true.
Example: For the inequality x > 3, all numbers that are less
than 3 make the inequality true.
Remember the Signs of Inequality
> Greater than
< Less than
= Equal to
 Less than and equal to
 Greater than and equal to
Practice Understanding Inequalities
Is each number a solution of x > 5?
a. –2
No, –2 > 5 is not true.
b. 10
c. 25
Yes, 10 > 5 is true.
Yes, 5 > 5 is true.
Is each number a solution of 3 + 2x < 8?
a. –2
3 + 2x < 8
b. 3
3 + 2x < 8
3 + 2(–2) < 8 Substitute for x.
3 + 2(3) < 8
Substitute for x.
–1 < 8
–2 is a solution.
3 is not a solution.
Representing Inequalities on a Number Line
An inequality may have more than one solution.
Use the following symbols to graphically represent solutions
to an inequality.
Closed dot on a number line shows solution includes value
Open dot on a number line shows solution does not
include value
a. Graph d < 3.
The solutions of d < 3
are all the points to the
left of 3.
b. Graph –3 ≥ g.
The solutions of –3 > g
are –3 and all the points
to the left of –3.
Writing Inequalities from Number Lines
Numbers less than 2 are graphed.
x < –3
Numbers less than or equal to –3
are graphed.
x > –2
x >
Numbers greater than –2 are
Numbers greater than or equal to 1
are graphed.
Write an Inequality for each Situation
a. A speed that violates
the law when the
speed limit is 55
miles per hour.
Let v = an illegal speed.
The speed limit is 55,
so v > 55.
b. A job that pays
at least $500 a
Let p = pay per month.
The job pays $500
or more,
so p > 500.
How would you graph the solutions to the above problems on
a number line?
Real World: Using Inequalities
Suppose your school plans a musical. The goal is to
have ticket sales of at least $4000. Adult tickets are
$5.oo and student tickets are $4.00. Let a represent the
number of adult tickets and s represent the number of
student tickets.
Write an inequality that represents the school’s goal.
5a + 4s  4000