Transcript 1. - TeacherWeb

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
Vocabulary
inequality
solution of an inequality
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
An inequality like 3 + x < 9
has too many solutions to
list. You can use a graph on
a number line to show all
the solutions.
The solutions are shaded and an arrow shows that
the solutions continue past those shown on the
graph. To show that an endpoint is a solution, draw a
solid circle at the number. To show an endpoint is
not a solution, draw an empty circle.
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Helpful Hints…
• When the variable is on the LEFT
side of the inequality, shade in the
direction the arrow is pointing…
< “points to the left”
> “points to the right”
• < and > - OPEN CIRCLE
• < and > - CLOSED CIRCLE
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Example 2: Graphing Inequalities
Graph each inequality.
A. m ≥
–
0
Draw a solid circle at
1
2
3
3
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
8
10 12
.
Shade all the numbers
greater than and draw an
arrow pointing to the right.
Simplify.
Draw an empty circle at
10.
Shade all the numbers
less than 10 and draw an
arrow pointing to the left.
3-1 Graphing and Writing Inequalities
Check It Out! Example 2
Graph each inequality.
Draw an empty circle at 2.5.
a. c > 2.5
2.5
–4 –3 –2 –1
0
1
2
3
4
5
6
b. 22 – 4 ≥ w
22 – 4 ≥ w
4–4≥
w 0≥w
–4 –3 –2 –1 0
1
Draw a solid circle at 0.
Shade in all numbers less than 0 and
draw an arrow pointing to the left.
2
3
4
5
6
c. m ≤ –3
Draw a solid circle at –3.
−3
–8 –6 –4 –2
Holt Algebra 1
0
Shade in all the numbers greater
than 2.5 and draw an arrow pointing
to the right.
2
4
6
8
10 12
Shade in all numbers less than –3
and draw an arrow pointing to the left.
3-1 Graphing and Writing Inequalities
Example 3: Writing an Inequality from a Graph
Write the inequality shown by each graph.
x<2
Use any variable. The arrow points to the left, so use
either < or ≤. The empty circle at 2 means that 2 is
not a solution, so use <.
x ≥ –0.5
Use any variable. The arrow points to the right, so
use either > or ≥. The solid circle at –0.5 means
that –0.5 is a solution, so use ≥.
Holt Algebra 1
3-1 Graphing and Writing Inequalities
Check It Out! Example 3
Write the inequality shown by the graph.
x < 2.5
Holt Algebra 1
Use any variable. The arrow
points to the left, so use either <
or ≤. The empty circle at 2.5
means that 2.5 is not a solution,
so use so use <.
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
Example 4: Application
Ray’s dad told him not to turn on the air
conditioner unless the temperature is at least
85°F. Define a variable and write an inequality
for the temperatures at which Ray can turn on
the air conditioner. Graph the solutions.
Let t represent the temperatures at which Ray can
turn on the air conditioner.
Turn on the AC when temperature
t
≥
t  85
70
75
Holt Algebra 1
80
85
is at least 85°F
90
85
Draw a solid circle at 85. Shade
all numbers greater than 85 and
draw an arrow pointing to the
right.
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 wages.
An employee earns
at least
w
≥
w ≥ 8.5
−2 0
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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