Transcript Chapter 2 Equations and Inequalities

Chapter 2
Equations and Inequalities
2.1 More on Solving Equations
Objective: Solve equations containing fractions or decimals.
When an equation contains fractions or decimals, we can use the
multiplication property to eliminate them. The process is called
clearing the equation of fractions or decimals.
Solving an Equation with Decimals
Solve the equation by clearing it of all decimals first.
Solve the equation by clearing it of all fractions or
decimals first.
A
B
C
Objective: Use the principle of zero products to solve equations.
Solving an Equation with Zero Products
Solve ( x  3)( x  2)  0
Solve 2 x( x  1)  0
Solving an Equation with Zero Products
Solve (2 x  5)(5 x  1)  0
Solving an Equation with Zero Products
Solve the equation using the zero products property.
D (2 x  4)( x  4)  0
E x(2 x  16)  0
Solving an Equation
Solve the equation
x( x  4)  x( x  4)
Solving an Equation
Solve the equation
3
1
( x  4)  4(2 x  5)  4( x  4)  (2 x  5)
5
2
2.2 Using Equations
Objective: Solve problems by translating to equations.
Objective: Solve problems by translating to equations.
A 23-ft cable is cut into two pieces, one three times as
long as the other. How long are the pieces?
Herman is doing an experiment that calls for a 40%
solution of copper sulfate. He has a 60ml of a solution
that is 25% copper sulfate. How many milliliters of a
70% solution should Herman add to obtain the required
40% solution?
Two cars leave the 7-11 at the same time going in the
same direction. One car is going 45 mph and the other
car is going 58 mph. In 2.5 hours how far apart are they?
A popular music CD was discounted 25% to $8.42. What
was the original price?
Write an equation and use it to solve the following
F
A tank at a marine exhibit contains 2000
gallons of sea water. The sea water is 7.5%
salt. How many gallons, to the nearest
gallon, of fresh water must be added to the
tank so that the mixture contains only 7%
salt?
HW #2.1-2
Pg 64 15-41 Odd, 42-46
Pg 70 19-27 Odd
HW Quiz #2.1-2
Monday, March 28, 2016
Pg 64 41
Pg 64 44
Pg 70 25
Pg 70 27
Pg 64 39
Pg 64 42
Pg 70 21
Pg 70 27
2.3 Solving Formulas
Objective: Solve a formula for a specified letter.
A formula is a rule for doing a specific calculation.
Solving a Formula for a specific variable
Solving a Formula for a specific variable
Solving a Formula for a specific variable
Solving a Formula for a specific variable
1 1 1 1
Solvefor x :   
z y x w
A: Solvefor r : Q  3r  5 p
B: Solvefor p : A  p  p r t
2.4 Solving Inequalities
Objective: Determine if a number is a solution of an inequality and graph
the solution set.
If a number occurs to the left of another on the number line, the
first number is less than the second, and the second is
greater than the first.
2  3
3  2
Objective: Solve and graph inequalities using the addition property.
Objective: Solve and graph inequalities using the multiplication property.
Solving an Inequality
( x  3)( x  2)  0
( x  4)( x  5)  0
Solving an Inequality
x3
0
x 3
x4
0
x 3
G ( x  4)( x  5)  0
x4
F
0
x3
HW #2.3-4
Pg 72 17-23 Odd, 25-31
Pg 77 19-27 Odd, 28-38
HW Quiz #2.3-4
Monday, March 28, 2016
Pg 72 26
Pg 72 28
Pg 77 30
Pg 77 34
Pg 72 28
Pg 72 30
Pg 77 32
Pg 77 36
2.5 Using Inequalities
Suppose that a machinist is manufacturing boxes of various sizes with
rectangular bases. The length of a base must exceed the width by at least
3 cm, but the base perimeter cannot exceed 24 cm. What widths are
possible?
2.6 Compound Inequalities
Objective: Solve compound inequalities.
A compound inequality is two simple inequalities joined
by “and” or “or.”
Statements involving the
word “and” are called
conjunctions.
For a conjunction to be true
all individual statements
must be true
Statements involving the
word “or” are called
disjunctions.
A disjunction is true when at
least one of the statements is
true
Conjunctions
2  x and x  3
x  2 and x  3
In mathematics, conjunction is called intersection and is symbolized by
the symbol: 
Disjunctions
x  2 or x  3
2  x or x  3
In mathematics, disjunction is called union and is symbolized by the
symbol: 
Solve the following inequalities. Graph your solution on a number
line and write them in interval notation.
A  4  3( x  2)  2
3
3
B x  1  0 or x  1  5
2
2
C 22  50 x  20  68
D x  1  5 or x  1  3
Write and solve a compound inequality that is
the conjunction of two disjunctions.
Write an inequality that has no solution and
show it has no solution.
Write an inequality whose solutions are all real
numbers and show why the solutions are all
real numbers.
HW #2.5-6
Pg 81 10-18
Pg 85-86 1-31 Odd, 33-45
HW Quiz #2.5-6
Monday, March 28, 2016
Row 1, 3, 5
Row 2, 4
Solve Write answer
in interval notation
-2 < 3x – 4 < 8
Solve Write answer in
interval notation
-2 < 3x – 4 or 3x – 4 ≤ 8
Solve Write answer
in interval notation
-4 < 3x – 4 < 8
Solve Write answer in
interval notation
-4 < 3x – 4 or 3x – 4 ≤ 8
2.7 Absolute Value
|2| = |-2| = 2
Objective: Simplify absolute value expressions.
Objective: Find the distance between two points using absolute value.
Objective: Solve and graph equations and inequalities involving absolute
value.
Objective: Solve and graph equations and inequalities involving absolute
value.
Objective: Solve and graph equations and inequalities involving absolute
value.
Objective: Solve and graph equations and inequalities involving absolute
value.
Objective: Solve and graph equations and inequalities involving absolute
value.
Objective: Solve and graph equations and inequalities involving absolute
value.
Objective: Solve and graph equations and inequalities involving absolute
value.
| x  1|| x  2 |
| x  1|| x  2 |
x  5  2x 1
Objective: Solve and graph equations and inequalities involving absolute
value.
HW #2.7
Pg 91 1-37 Odd, 38-51
HW Quiz #2.7
Monday, March 28, 2016
Row 1, 3, 5
Solve
|2x – 3| > 5
Solve
|2x – 3| < 11
|3x – 2| < 10
Row 2, 4
Solve
|3x – 2| > 6
2-8 Proofs in Solving Equations
Test 1-2
• Part 1-5Questions
• 2-proofs
– Any Proof in the HW
– Any Proof I did in class
• 1-Closure
• 2 questions with no numbers
Objective: Prove conditional statements.
Conditional Statements
P Q
Antecedent
Hypothesis
Consequence
Conclusion
To prove a conditional statement you assume the Hypothesis and Show
the conclusion must also be true.
Use a two column proof or narrative proof
Objective: Write and prove the converse of a conditional statement.
P Q Q  P
Conditional
Statement
Converse of
the Conditional
Statement
To prove a the converse of a conditional statement you assume the
Conclusion and Show the Hypothesis must also be true.
Objective: Solve equations and inequalities by proving a statement and
its converse.
P  Q and Q  P
PQ
Biconditional
HW #2.8
Pg 96-97 1-21 Odd, 23-32
Test Review Topics
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Simplify – Order of Operations
Solve Equations
Exponents – Multiply/Divide – Negative Exponents
Word Problem
Compound Inequalities – Interval Notation
Absolute Value
Sign Charts
Solve for a Variable
Factoring – to solve quadratics
| x  5 || 2 x  1 |
2  | 2 x  10 |  8
x2
0
( x  3)( x  1)
x y
p
xy
x  7 x  36  2 x
2
A suitcase of money contains b hundred dollar bills. After the bills are
distributed evenly among g federal agents, 8 hundred dollars bills are left
over. In terms of b and g, how many hundred dollar bills did each agent
get?
If a Citation Jet travels at an average speed of x miles per hour, how
many hours would it take the Citation to travel 800 miles?
HW R1-2
• Study Hard
Find the area of an equilateral triangle