Download Page 1 What symbol is this? Objective

Lesson 3-1
Objective - To recognize and graph simple
inequalities.
Equalities
= Equals - Is the same as
What symbol is this?
≅ Congruent - Same size
>
17.2
0.985
and same shape
∼ Similar - Same shape
Many students can’t tell them apart.
reater than
>
<
ess than
1)
-1
0
1
2
3
4
2)
5
3)
4)
2) x > −3
-5 -4
5)
-3 -2
-1
0
1
2
3
4
6)
5
7)
Inequality
Symbol
Example
<
Is less than
x<4
0
4
>
Is greater than
y > −3
-3
0
Is less than
or equal to
n ≤ −4
-4
0
Is greater than
or equal to
k≥5
0
5
≥
equal to
≥ Is greater than or
equal to
≈ Is approximately
equal to
≥
<
=
≤
>
≈
≠
“is greater than or equal to”
“is less than”
“is equal to”
“i less
“is
l than
th or equall to”
t ”
“is greater than”
“is approximately equal to”
“is not equal to”
Write an inequality to represent each sentence.
Phrase
≤
≤ Is less than or
Identify each symbol below.
1) x ≤ 2
-3 -2
> Is greater than
≠ Is not equal to
How can you graphically show the following?
-5 -4
Inequalities
< Is less than
Graph
1) A number x is more than 18.
x > 18
2) A number y is less than or equal to -12.
y ≤ −12
3) Twice a number x is less than 5.
2x < 5
4) Eight more than twice a number p is less than
or equal to 40.
2p + 8 ≤ 40
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
Lesson 3-1 (cont.)
Tricky Ones!
Write an inequality to represent each sentence.
Phrase
Inequality
x is at least 5
x≥5
y is at most 10
y ≤ 10
p is no more than 6
p≤6
n is no less than 8
n≥8
1) Twice a number x plus four is at least 10.
2x + 4 ≥ 10
2) Five less than 3 times y is at most 19.
3y − 5 ≤ 19
3) Twice the sum of x and 9 is no more than 35.
2(x + 9) ≤ 35
4) Fifteen is less than 6 times the difference of
p and 7.
15 < 6 ( p − 7 )
Write an inequality that describes each graph below.
Phrases that are often confused
Phrase
1) x < 2
Translation
5 more than x
x+5
5 is more than x
5> x
x less 8
x −8
x less than 8
8− x
x is less than 8
x<8
x is at least 8
x≥8
-2
8
0
2
3
7
-6
0
9
-1
0
0
1
2
3
4
5
-3 -2
-1
0
1
2
3
4
5
3
4
5
3) All real numbers less than -4.
x < −4
-5 -4
-8
-1
x<4
4) m ≤ −1
-6
-3 -2
2) All whole numbers less than 4.
0
-1
0
Write an inequality that represents each statement
and graph.
1) All real numbers less than or equal to 3.
-5 -4
-4
-24
x≤3
3) m > −4
-3
15
6) x ≤ −24
3
8
0
-4 -3 -2 -1 0 1 2 3 4
-5 -4
-77
5) x ≥ 15
3) x > 0
2) y ≥ 3
6
0
-4 -3 -2 -1 0 1 2 3 4
1) x < 5
5
-9
2) x ≥ −1
Circle each solution for the given inequalities.
4
4) x > −9
-4 -3 -2 -1 0 1 2 3 4
-3 -2
-1
0
1
2
3
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
Lesson 3-1 (cont.)
Write an inequality that represents each statement
and graph.
4) A number x is at least 2.
x≥2
-5 -4
-3 -2
-1
0
1
2
3
4
5
Translate each sentence below.
1) Five more than x is greater than or
equal to 19.
x + 5 ≥ 19
2) Sixteen less than y is less than 4 less y.
5) A number y is less than -2.
y − 16 < 4 − y
y < −2
-5 -4
-3 -2
-1
0
1
2
3
4
5
11 ≤ m ÷ 8 or 11 ≤
6) An integer p is no more than 4.
p≤4
-5 -4
-3 -2
-1
0
3) Eleven is less than or equal to the quotient
of m and 8.
m
8
4) Seven is at least one more than twice x.
1
2
3
4
5
7 ≥ 2x + 1
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010