Download 1. Solve: 4(x – 3) – 10 = 4 – 3(x + 4) 3. Find three consecutive odd

1. 
2. 
3. 
4. 
5. 
Solve: 4(x – 3) – 10 = 4 – 3(x + 4)
2 1
1
Solve: 3 ( 5 x − 3) = − 2 (3x +5)
Find three consecutive odd
numbers such that 4 less than twice
the third is equal to the difference
between the second and the first.
Determine if -1/2 is a solution to
4x – 3 < -12 ?
Solve: 2x + 1 ≤ 6x – 1
Algebra II
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Solving Inequalities and
Compound Inequalities
Algebra II
¡  Inequality
§  a mathematical sentence that contains
an inequality symbol.
¡  Solution
§  a number that makes the sentence true.
Algebra II
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¡  Isolate
the variable!
¡  Don't
forget to flip the inequality
symbol if you multiply or divide
by a negative
¡  Always
write the variable on the
left when finished with the
problem.
Algebra II
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Inequality
Notation
x<#
x<#
x>#
x>#
Algebra II
Graph
)
]
(
[
)
Interval
Notation
(-∞ , # )
(-∞ , # ]
(#,∞)
[#,∞)
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1. 3 < 2/3 x + ½
2. 7x + 9 ≥ 10x – 12
18 < 4x + 3
-3x ≥ -21
15 < 4x
x≤7
15/4 < x
(-∞, 7]
x > 15/4
( 15/4, ∞)
Algebra II
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3. 1/3(5/8x + 2) ≥ 2/3 x + 2 4. 4(1/2x + 7/3) > 1/3(x + 12)
5/24x + 2/3 ≥ 2/3x + 2
2x + 28/3 > 1/3x + 4
24[5/24x + 2/3 ≥ 2/3x + 2]
3[2x + 28/3 > 1/3x + 4]
5x + 16 ≥ 16x + 48
6x + 28 > x + 12
-11x ≥ 32
5x > -16
x ≤ -32/11
x > -16/5
( -∞, -32/11]
(-16/5, ∞)
Algebra II
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¡ 
¡ 
Two Inequalities connected by “and” or ”or”
“And”: intersection
§  Both statements must be true.
§  When graphing, shade where the two statements
overlap
¡ 
“Or”: Union
§  Either statement can be true.
§  When graphing, shade anything that is graphed
Algebra II
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1. -2 ≤ 3x - 8 ≤ 10
+8
+ 8 +8
6 ≤ 3x ≤ 18
3 3
3
Algebra II
2. -9 < 2x + 3 < 10
-3
-3 -3
-12 < 2x < 7
2
2 2
2≤x≤6
-6<x<7/2
[2, 6]
(-6, 7/2)
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3. 3x - 2 ≥ 10 or -4x ≥ 16
+2 +2
-4
-4
3x ≥ 12
x ≤ -4
x≥4
or
x ≤ -4
(-∞, -4] U [4, ∞)
Algebra II
4. 2x + 3 < 5 or 4x - 7 > 9
-3 -3
+ 7 +7
2x<2
x<1
or
4x > 16
or
x>4
(-∞, 1) U (4, ∞)
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5. 8 < 3x – 1 < -2
+1
+1 +1
9 < 3x
3
3
< -1
3
3 < x < - 1/3
Algebra II
What numbers are
greater than 3 AND
less than -1/3?
No Solution
( An “and” that
doesn’t overlap)
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6. 2x + 6 < 16 or ½ x + 3 > -5
-6 -6
-3 -3
2x < 10 or
2
2
x<5
or
Algebra II
½ x > -8
½
½
x > -16
What numbers are less
than five OR greater
than -16.
All Real Numbers
An “or” that overlaps
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1. When 5 times a number is subtracted
from 6, the result is at least 26.
X is less than or equal to -4
Algebra II
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2. With a golf club membership costing $100 per
month, each round of golf costs only $25.00. How
many rounds of golf can a member play if he wishes
to keep his costs to $250 per month at most?
With a golf club membership costing $100 per month, each round of golf costs only $25.00. How many
rounds of golf can a member play if he wishes to keep his costs to $250 per month at most?
X is less than or equal to 6
Algebra II
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3. To get a grade of C in your course, you must average
at least 75% on 4 exams. You have taken the first three
exams and gotten scores of 68, 78, and 81. What must
you score on the last exam to get a C or better?
X is greater than or equal to 73
Algebra II
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4. 
You have just been given a new job in sales. You have two
salary options. You can receive a straight salary of $500
per week (no commission option) or you can receive a
salary or $200 per week plus 5% of your weekly sales
(commission option). What dollar amount of product must
you sell each week in order for the commission option to
be the better deal?
X is greater than 6,000
Algebra II
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1. 
2. 
When do you use parentheses in interval notation?
Brackets?
What order do you write interval notation?
3. 
What punctuation to you use for + infinity?
4. 
What is different between solving an equation and an
inequality?
5. 
What does an and compound inequality mean? or?
Algebra II
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