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Warm-up 10/14/2010. Simplify. 1.) 5(7x – 12) 2.) (–3 – 4p)(3) 3.) 4 - 2(–6y + 2). Algebra 1 Chapter 3 Sections 1-5. PE: A1.1.B Solve Problems that can be represented by linear functions, equations, and inequalities. Vocabulary. Equivalent: has the same value, “is equal” - PowerPoint PPT Presentation
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Simplify. 1.) 5(7x – 12) 2.) (–3 – 4p)(3) 3.) 4 - 2(–6y + 2)
Warm-up 10/14/2010
Algebra 1 Chapter 3 Sections 1-5
PE: A1.1.B Solve Problems that can be represented by linear functions, equations,
and inequalities.
Equivalent: has the same value, “is equal” Inverse Operations: operations that undo
each other. Linear Equation: An equation where the
variable (or variables) are raised to the first power, do not occur in the denominator, inside a square root, or inside absolute value symbols.
Example: 3x-2=27 is a linear equation
Vocabulary
Are the following Linear Equations? Why?
x + 5 = 9 yes
x2 + 5 = 9 no
-4 + n = 2n - 6 yes
|x + 3| = 7 no
Linear or Not?
( ) distribute • Can you combine like terms on the LHS? ____ (do it!) • Can you combine like terms on the RHS? ____ (do
it!) • If variables are on both sides, then make one go
away. • What side of the new equation is the variable on?
____ • Is there a number being added or subtracted to
THAT side? ___ (get rid of it! Do the opposite.) • Is there a number “next to” the variable? _____
(get rid of it! DIVIDE.)
Solve x - 5 = -13 for x.
Examples
Solve -8 = n - (-4)
Examples
Simplify. 1.) -5(6x – 11)
2.) (3 – 7p)(-2)
3.) 4 - 2(–7y - 2)
Entry Task 10/20/2011
Solve x – 7 = 13 for x.
Solve 3 – (-x) = 12 for x.
Exit Task
Solve using multiplication and division
1.) 2.)
3.) 4x = 12 4.)
Entry Task 10/24/2011
32
x
m3210
305
x
Classify the following numbers as Real, Irrational, Rational, Integers, whole numbers , or natural
1.) 4 2.) ¾ 3.) -2
Exit Task
Chapter 2 test Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between
you and your neighbor. Make sure you have a pencil, calculator and
eraser to take the quiz.
Simplify. 1.)
Solve 2.) 3.)
Entry Task 10/26/2011
34)43(
65
x
552
x 8631
x
The usual rate for taking and projecting professional movies is 24 frames per second. Find the total number of frames in a movie that is 90 minutes long.
Exit Task
Simplify:
1.) 2.)
3.) 4.)
5.)
Entry Task 10/27/2011
)3(56
x)4(35 xx
837 xx )2(34 xx
Simplify the following: 1.) -6(x+5) 2.) (r-3)(-4)
3.) m(m-1) 4.) (-2a)(a+3)
5.) Write an expression for the perimeter of the trapezoid shown below and simplify it
Entry Task 10/28/2011
Homework Questions?
Pg. 148 #1-9, 11-35odd, due 10/21
Extra Credit Pg. 148 # 10-36 even, 57-61
Homework
Simplify:
1.) 2.)
Determine whether the given number is a solution to the equation or inequality.
3.) 8+r2 = 16; 4 4.) 2(5y-4)=14; 7.5
5.)
Entry Task 11/01/2011
xx 23334
xx )13(
Entry Task 11/02/2011 Evaluate the following for x=21.) 2x+7 2.) 5x2 + 2
3.) 3[(x-2)+x] 4.) 3(x-8)x
Determine whether the given number is a solution to the equation or inequality.
5.) 8+r2 = 16; 2 6.) 2(5y-4)=14; 2.2
Entry Task 11/03/20111.)
2.)
3.)
4.)
5.)
6.)
Chapter 2 test retake (again) Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between
you and your neighbor. Make sure you have a pencil, calculator and
eraser to take the quiz.
Equations can have zero, one or many solutions.
Equations with one solution can be worked out to equal one number.
Number of Solutions
552197 xx
If the variables cancel out and the numbers left are not equal there are no solutions
NO Solution
42 xx
If the variables cancel out and the two sides of the equal sign are equal then there are many solutions, in fact x would be all real numbers.
Many solutions
63)2(3 xx
Homework Questions?
Evaluate the following for x=51.) 2x+7 2.) 5x2 + 2
3.) 3[(x-2)+x] 4.) 3(x-8)x
Determine whether the given number is a solution to the equation or inequality.
5.) 8+r2 = 16; 5 6.) 2(5y-4)<14; 2
Solve.7.) 8.)
Entry Task 11/14/2011
63)2(3 xx 42 xx
Objective: Solve a formula for one of its variables.
Section 3.7
The formula for the area of a rectangle is A=lw
Find a formula for l in terms of A and w.
Solving Formulas
Rewrite the equation so that x is a function of y
Rewriting an Equation in Function Form
43 yx
Entry Task 11/15/2011
552197 xx213)2(6 xx
Simplify:
1.) 2.)
3.) 4.)
Solve:
5.)
6.)
)3(56
x)4(35 xx
837 xx )2(34 xx
Entry Task 11/16/20111.)
2.)
3.)
4.)
5.)
6.)
Solve using multiplication and division
1.) 2.)
3.) 4x = 12 4.)
5.) Decide if the following are functions, state the domain and range if they are.
Entry Task 11/28/2012
32
x
m3210
305
x
1234
Input Output2
4
5
Input Output1234
57
9
Entry Task 11/18/2011
552197 xx213)2(6 xx
Simplify:
1.) 2.)
3.) 4.)
Solve:
5.)
6.)
)3(56
x)4(35 xx
837 xx )2(34 xx
Identifying functions A relation is any set of ordered pairs. A Function is a relation where for every
input there is exactly one output.
f(x) is read “f of x” or “the value of f at x”. It Does not mean f times x
f(x) is called function notation.
Write y = 3x + 2 in function notation
Function notation f(x) is read “f of x” or “the value of f at x”. It
Does not mean f times x f(x) is called function notation.
Write y = 3x + 2 in function notation
a.) b.)
Examples
552197 xx 213)2(6 xx
a.) b.)
Examples
yy 6980 ww 6)316(4
a.) b.)
Examples
)1(23)1(4 xxx )2(310)1612(41
xx
Solve:
1.) 2.)
Entry Task 10/22/2010
96)43(2 xxxx 414217
Homework Questions?
Quiz
When finished with Quiz quietly work on:
Agenda for today
Pg. 157#1-11, 19-250ddExtra Credit pg. 157 #12-40 even, 47=49
Solve:
1.) 2.)
Entry Task 10/25/2010
16)2(4 x18538 xx
Objective: Solve problems using linear equations
Section 3.5
ExampleGAZELLE AND CHEETAH
A gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second) but can only sustain its top speed for about 20 seconds before it is worn out. How far away from the cheetah does the gazelle need to stay for it to be safe?
ExampleA pate of your school yearbook is 8 ½ inches by 11 inches. The left margin is ¾ inch and the space to the right of the pictures is 2 7/8 inches. The space between pictures is 3/16 inch. How wide can each picture be to fit three across the width of the page?
Pg. 163 #1-5
Extra Credit pg. 163 #18-21, 27
Homework
Solve:
1.) 2.)
Entry Task 10/27/2010
xx 313)2(4 xx 21838
Objective: Solve problems using linear equations
Section 3.5
Pg. 163 # 6-13E.C. 14-17, 23-26
Homework
Solve:
1.) 2.)
3.) Round the following numbers to the indicated Place value.
a.) 1041, tens placeb.) -3.755, hundreds place
Entry Task 10/28/2010
yy 2)4(10 5647 mm
Objective: Find exact and approximate solutions of equations that contain decimals.
Section 3.6
Three people want to share equally in the cost of a pizza. The pizza costs $12.89. How much should each person pay?
Rounding for Practicality
Solve 3.58x-37.40=0.23x=8.32. Round to the nearest hundredth.
Original equation with decimals
Pg. 169 #1-13 skip #2
E.C. 14-38 even
Homework
Solve:
1.) 2.)
3.) Round the following numbers to the indicated Place value.
a.) 1041, tens placeb.) -3.755, hundredths place
Entry Task 10/29/2010
yy 3.22.4 1.54.63.45.7 mm
A=1/2bh is the formula for the area of a triangle. Solve this formula for b, the base of the triangle.
Solve 3x+5 = 20 for x
Entry Task 11/01/2010
Objective: Rewrite an equation in function form.
Section 3.7 cont.
rewrite the following equations so that y is a function of x
Entry Task 11/02/2010
16412 yx 20155 xy
Get out your planner and write the following homework assignment in for today:◦ Pg. 371 #17-28 due Monday
Solve:
Entry Task 11/05/2010
)74(210824 aaa
Pg. 193 #1-21This is worth a quiz grade
Practice test