### Chapter 3 Power Point

```Simplify.

1.) 5(7x – 12)

2.) (–3 – 4p)(3)

3.) 4 - 2(–6y + 2)
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
Are the following Linear Equations? Why?
x + 5 = 9 yes
x2 + 5 = 9 no
-4 + n = 2n - 6
|x + 3| = 7 no
yes

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
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


( ) 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.

Solve -8 = n - (-4)
Simplify.

1.) -5(6x – 11)

2.) (3 – 7p)(-2)

3.) 4 - 2(–7y - 2)

Solve x – 7 = 13 for x.

Solve 3 – (-x) = 12 for x.

Solve using multiplication and division

1.)
x
3
2
2.)

3.) 4x = 12
4.)
2
10   m
3
x
 30
5


Classify the following numbers as Real,
Irrational, Rational, Integers, whole numbers ,
or natural
1.) 4
2.) ¾
3.) -2




Make sure there is at lease 1 foot between
Make sure you have a pencil, calculator and
eraser to take the quiz.
Simplify.

1.)
5
4
(3 x  4) 
6
3
Solve 2.)
2
x5
5
3.)
1
x  6  8
3

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.

Simplify:

1.)
5 x  3( x  4)

3.)
7 x  3x  8

5.)
2.)
4.)
6
 ( x  3)
5
4 x  3( x  2)

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
 Pg.
148 #1-9, 11-35odd, due
10/21
 Extra
Credit Pg. 148 # 10-36
even, 57-61


Simplify:
1.)
(3x  1)  x
2.)
4x
 3  23 x
3
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.)
Evaluate the following for x=2
1.) 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

1.)
2.)
3.)
4.)
5.)
6.)




Make sure there is at lease 1 foot between
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.
7 x  19  2 x  55

If the variables cancel out and the numbers
left are not equal there are no solutions
x2 x4

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.
3( x  2)  3x  6
Evaluate the following for x=5
1.) 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.) 3( x  2)
 3x  6
8.)
x2 x4

Objective: Solve a formula for one of its
variables.


The formula for the area of a rectangle is
A=lw
Find a formula for l in terms of A and w.

Rewrite the equation so that x is a function of
y
3x  y  4

Simplify:

1.)
5 x  3( x  4)

3.)
7 x  3x  8

Solve:

5.)

6
(
x

2
)


3
x

21
6.)
7 x  19  2 x  55
2.)
4.)
6
 ( x  3)
5
4 x  3( x  2)
1.)
2.)
3.)
4.)
5.)
6.)




Solve using multiplication and division
x
3
2
2.)
3.) 4x = 12
4.)
1.)
2
10   m
3
x
 30
5
5.) Decide if the following are functions, state
the domain and
range if they are.
Input
1
2
3
4
Output
2
4
5
Input
1
2
3
4
Output
5
7
9

Simplify:

1.)

3.)

Solve:

5.) 7 x  19

6.)
2.)
5 x  3( x  4)
7 x  3x  8
 2 x  55
6( x  2)  3x  21
4.)
6
 ( x  3)
5
4 x  3( x  2)


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


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.)
7 x  19  2 x  55
b.)
6( x  2)  3x  21
a.)
80  9 y  6 y
b.)
4(16  3w)  6w
a.) 4(1  x)  3x  2( x  1)
1
b.) (12 x  16)  10  3( x  2)
4

Solve:

1.)
17  2 x  14  4 x
2.)
2(3x  4)  6 x  9

Quiz

When finished with Quiz quietly work on:
Pg. 157#1-11, 19-250dd
Extra Credit pg. 157 #12-40 even,
47=49

Solve:

1.)
8 x  3  5 x  18
2.)
4( x  2)  16

Objective: Solve problems using linear
equations
GAZELLE 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?
A 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

Solve:

1.)
8 x  3  18  2 x
2.) 4( x  2)  13  3x

Objective: Solve problems using linear
equations
Pg.
163 # 6-13
E.C. 14-17, 23-26

Solve:

1.)
 7  4m  6m  5
2.)
10(4  y)  2 y
3.) Round the following numbers to the indicated
Place value.
a.) 1041, tens place
b.) -3.755, hundreds place

Objective: Find exact and approximate
solutions of equations that contain decimals.

Three people want to share equally in the
cost of a pizza. The pizza costs \$12.89. How
much should each person pay?

Solve 3.58x-37.40=0.23x=8.32. Round to
the nearest hundredth.
Pg.
169 #1-13
skip #2
E.C.
14-38 even

Solve:

1.)  7.5  4.3m  6.4m  5.1 2.)
 4.2  y  2.3 y
3.) Round the following numbers to the indicated
Place value.
a.) 1041, tens place
b.) -3.755, hundredths place


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

Objective: Rewrite an equation in function
form.

rewrite the following equations so that y is a
function of x
12x  4 y  16
5 y  15x  20

Get out your planner and write the following
homework assignment in for today:
◦ Pg. 371 #17-28 due Monday
Solve:
24a  8  10a  2(4  7a)
Pg.
193 #1-21
This is worth a