Download 3-5 - mathppt.com

Lesson 3-5
Objective - To recognize and to graph
inequalities.
Equalities
Inequalities
< Is less than
= Equals - Is the same as
How can you graphically show the following?
1) x ≤ 2
-5 -4
> Is greater than
≅ Congruent - Same size
-3 -2
-1
0
1
2
3
4
5
-3 -2
-1
0
1
2
3
4
5
≤ Is less than or
and same shape
equal to
≥ Is greater than or
equal to
≈ Is approximately
equal to
∼ Similar - Same shape
2) x > −3
-5 -4
≠ Is not equal to
Inequality
Symbol
Write an inequality to represent each sentence.
Phrase
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
≤
≥
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
Tricky Ones!
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
Write an inequality that represents each statement
and graph.
1) All real numbers less than or equal to 3.
x≤3
-5 -4
-3 -2
-1
0
1
2
3
4
5
3
4
5
3
4
5
2) All real numbers greater than -2.
x > −2
-5 -4
-3 -2
-1
0
1
2
3) All real numbers less than -4.
x < −4
-5 -4
-3 -2
-1
0
1
2
Pre-Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2011
Lesson 3-5 (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
-1
0
-4 -3 -2 -1 0 1 2 3 4
1
2
3
4
-1
0
1
2
3) x > 0
3
4
5
Write an inequality to represent each sentence.
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 )
6) x ≤ −24
-4 -3 -2 -1 0 1 2 3 4
-24
0
Phrases that are often confused
Phrase
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
Write a compound inequality that describes all
the real numbers less than -2 or greater than 5.
x < −2 or x > 5
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.
y − 16 < 4 − y
3) Eleven is less than or equal to the quotient
of m and 8.
m
11 ≤ m ÷ 8 or 11 ≤
15
Compound Inequalities
Translate each sentence below.
8
4) Seven is at least one more than twice x.
7 ≥ 2x + 1
0
5
x≤4
-3 -2
0
5) x ≥ 15
2) x ≥ −1
6) A number n is no more than 4.
-5 -4
-9
5
y < −2
-3 -2
4) x > −9
1) x < 2
-4 -3 -2 -1 0 1 2 3 4
5) A number y is less than -2.
-5 -4
Write an inequality that describes each graph below.
-3 -2
-1
0
1
2
3
4
5
6
Write a compound inequality that describes all
the real numbers greater than -2 and less than 5.
x > −2 and x < 5
“In-between
−2 < x < 5
statement”
-3 -2
-1
0
1
2
3
4
5
Pre-Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2011
6
Lesson 3-5 (cont.)
Write the following compound inequalities as
“In Between” statements.
1) x > −3 and x < 5
Describe each graph with a compound statement.
1) x > −5 and x < 9
-5
−3 < x < 5
0
or
−5 < x < 9
9
5 > x > −3
2) x ≤ −2 or x ≥ 15
2) x > 4 and x < 10
-2 0
4 < x < 10
3) x < −1 and x > −8
15
3) x ≤ −24 or x > 8
−8 < x < −1
-24
0
8
Describe each graph with a compound statement.
4) x > −3 and x ≤ 8
-3
0
or
−3 < x ≤ 8
8
5) x ≤ −11 or x > 35
-11 0
35
6) x ≥ −15 and x < 6
-15
0
or
−15 ≤ x < 6
6
Pre-Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2011