Transcript 2.1 PPT - Garnet Valley School District

2-1 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 of the
variable that makes the inequality true.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Reading Math
“No more than” means “less than or
equal to.”
“At least” means “greater than or
equal to”.
Holt McDougal Algebra 1
2-1 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
80
Holt McDougal Algebra 1
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.
2-1 Graphing and Writing Inequalities
Solving one-step inequalities is much like
solving one-step equations. To solve an
inequality, you need to isolate the variable
using the properties of inequality and
inverse operations.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Example 1A: Using Addition and Subtraction to Solve
Inequalities
Solve the inequality and graph the solutions.
x + 12 < 20
x + 12 < 20
–12 –12
x+0 < 8
x < 8
–10 –8 –6 –4 –2
0
Holt McDougal Algebra 1
2
Since 12 is added to x,
subtract 12 from both
sides to undo the
addition.
4
6
8 10
Draw an empty circle at 8.
Shade all numbers less
than 8 and draw an
arrow pointing to the
left.
2-1 Graphing and Writing Inequalities
Example 1C: Using Addition and Subtraction to Solve
Inequalities
Solve the inequality and graph the solutions.
0.9 ≥ n – 0.3
0.9 ≥ n – 0.3
+0.3
+0.3
1.2 ≥ n – 0
1.2 ≥ n
Since 0.3 is subtracted
from n, add 0.3 to both
sides to undo the
subtraction.
1.2
0
1

Holt McDougal Algebra 1
2
Draw a solid circle at 1.2.
Shade all numbers less
than 1.2 and draw an
arrow pointing to the
left.
2-1 Graphing and Writing Inequalities
Example 2: Problem-Solving Application
Sami has a gift card. She has already
used $14 of the total value, which was
$30. Write, solve, and graph an
inequality to show how much more she
can spend.
1
Understand the problem
The answer will be an inequality and a
graph that show all the possible
amounts of money that Sami can spend.
List important information:
• Sami can spend up to, or at most $30.
• Sami has already spent $14.
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Example 1C: Multiplying or Dividing by a Positive
Number
Solve the inequality and graph the solutions.
r < 16
0
2
4
6
Since r is multiplied by ,
multiply both sides by the
reciprocal of .
8 10 12 14 16 18 20
Holt McDougal Algebra 1
2-1 Graphing and Writing Inequalities
Check It Out! Example 1b
Solve the inequality and graph the solutions.
–50 ≥ 5q
Since q is multiplied by 5, divide
both sides by 5.
–10 ≥ q
–15
–10
–5
Holt McDougal Algebra 1
0
5
15
2-1 Graphing and Writing Inequalities
Example 3: Application
Jill has a $20 gift card to an art supply store
where 4 oz tubes of paint are $4.30 each after
tax. What are the possible numbers of tubes
that Jill can buy?
Let p represent the number of tubes of paint that Jill
can buy.
$4.30
times
4.30
•
Holt McDougal Algebra 1
number of tubes
is at most
$20.00.
p
≤
20.00
2-1 Graphing and Writing Inequalities
Lesson Quiz
Solve each inequality and graph the solutions.
1. 8x < –24 x < –3
2. –5x ≥ 30
x ≤ –6
3.
4.
x≥6
x > 20
5. A soccer coach plans to order more shirts for
her team. Each shirt costs $9.85. She has $77
left in her uniform budget. What are the
possible number of shirts she can buy?
0, 1, 2, 3, 4, 5, 6, or 7 shirts
Holt McDougal Algebra 1