Transcript 2012 Final Exam Study Guide

Trinomials are 3 sets of
numbers that are not alike
in any ways. In order to
solve trinomials, you need
to know your factors and
distributive property!
Try these examples:
x  12 x  27
2
x 2  13 x  42
To get x 2 , you have to multiply x times x
(x ) (x )
Since the last term is  , the signs will be the same as the
middle term.
(x  ) (x  )
Now, the factors of 42 are :
1 and 42, 2 and 21, 3 and 14, 6 and 7.
The right facor needs to equal to 13 when it' s added,
c  12 c  35
it also needs to be equal to 42 when it' s multiply!
(x  6) (x  7)
Use the distributi ve property!
x(x)  x(7)  6(x)  6(7)
y 2  13 y  30
x 2  7 x  6 x  42
combine like terms
d  7 d  10
x 2  13 x  42
2
2
Rose
Felisme
Finding the Equation of a Line
Given Two Points X Y
-3
Step 1: Find the slope of the line containing the points. 6
m= y2-y1
Slope formula
x2-x1
= -4-(-1)(x1,y1)=(-3,-1) and (x2,y2)=(6,-4)
6-(-3)
= -3 or-1
Simplify.
9 3
Step 2: Use the slope and one of the two points to find the yintercept.
y = mx+b Slope-intercept form
-4 = -1(6) + b Replace m with -1,x with 6, and y with -4.
3
3
-4 = -2 + b
Multiply.
-2 = b
Add 2 to each side.
Step 3: Write the slope-intercept form using m=-1 and b=-2
y = mx+b
Slope-intercept form
3
y = -1x-2
Replace m with -1, and b with -2.
3
3
-1
-4
Problems for you to try:
A. (2,3) (6,4) B. (2,4) (2,1)
C. (-1,12) (4,-8) D. (36,15) (22,10)
Description: If you
know two points on
a line, first find the
slope. Then follow
these steps…
•Use the slope and
one of the two
points to find the yintercept
•Write the slopeintercept form using
y=mx+b
•Check your answer
by graphing the line.
It should pass
through the two
points.
How to do it: The table shows the coordinates
of two points on the graph of a linear function.
Alexis
Clark
Simplifying square Roots using perfect
square
square Roots is a
quantity of which a given
quantity is the square.
Perfect squares are a
rational number that is
equal to the square of
another rational number.
EXAMPLE
81
2
y

9

y

9y
The first thing you need to know while
simplifying square roots using perfect
squares is if the number your dealing
with is a perfect square. In this case our
number is 81 and its a perfect square
because 9 times itself gives you 81.
The second thing you need to do is
find the square roots of y2 which
is y because y times itself is equal
to y2
Lastly you just put it all together
and the answer is 9y
Practice Problems
2
25
ba
36
b
22
169
ba
4
121
x
Kennie Rebecca
Solving inequalities using all
operations
An inequality can be use
when we don’t know
what an expression is
equal to… instead of an
equal sigh we an use this
symbol < ≥ > ≤
Four practice problems
1)5x-8<12
2)4-2x≤2x-4
3)-13m>-26
4)14g>56
For example:12x-4<8
12x<12(add 4 to each side of the inequality)
X<1 ( divide both sides of the inequality by 12)
One important rule you should always
remember if you multiplying or
dividing both sides of an inequality by
a negative number reverse the
direction of the inequality sigh
Tamarre Cynthia
Jabouin
2+4y > -6
2+4y < 6
-4 -3 -2 -1 0 1 2 3
Nia Rogers
Description:
A way to graph a equation in slopeintercept form, the equation is
y=mx+b: m is the slope and b is the
y-intercept and y and x is the points.
Slope is the steepness of the line
and intercept is where the line
connects and intersects with the y
For Example: axis.
y 5x4
1
y
x

(

5
) Slope
Intercept
Form
5
1
1
y
x

(

5
) slope
isand
y
intercept
is
5
5
5
First
Graph
intercept
and
the
then
slo
t
For
y9x3
Y intercept 4
Y intercept 3
Rise
Run
5
1
Example
1
y 
x  5
5
1
y 
x  3
 9
y   11 x  4
:
Fall-9
Run1
Gary Chen 5/31/12
Factoring a trinomial with leading coefficient other than 1
Description- This is one way to factor a polynomial. In this case there is a trinomial and also a
leading coefficient other that 1. Factoring this is the inverse of the distributive property that would
result in two binomials
Example 10d2 + 17d - 20
1 -multiply the numbers of the two outside terms and find factors that would equal the middle
term
10 x -20= -200
2- Find two fractions who’s sum add up to 17 -8 and 25 are factor of -200 that adds up to 17
3 substitute the middle term with the fractions 10d2-8d + 25d-20
4 is to split the problem so it is separated by the middle operation
(10d2-8d )+ (25d-20)
GCF= 5
GCF=2d
Find the GCF of both sides of the equation
3-Distribute the GCF to each of the terms to each equation using division instead of multiplying
2d(5d-4) + 5(5d-4)
Now add the outside terms and multiply it to the inside term (The terms inside the
parentheses should be the same in each part of the problem.
(2d-5) (5d-4) Answer
Practice Problems
By Jamari Robinson
2
10x +21x-10 12q2+34q-28
8z2+20z-48
12y2-4y-5
Factoring a trinomial with leading coefficient other than 1
Description- This is one way to factor a polynomial. In this case there is a trinomial and also a
leading coefficient other that 1. Factoring this is the inverse of the distributive property that would
result in two binomials
Example 10d2 + 17d - 20
1 -multiply the numbers of the two outside terms and find factors that would equal the middle
term
10 x -20= -200
2- Find two fractions who’s sum add up to 17 -8 and 25 are factor of -200 that adds up to 17
3 substitute the middle term with the fractions 10d2-8d + 25d-20
4 is to split the problem so it is separated by the middle operation
(10d2-8d )+ (25d-20)
GCF= 5
GCF=2d
Find the GCF of both sides of the equation
3-Distribute the GCF to each of the terms to each equation using division instead of multiplying
2d(5d-4) + 5(5d-4)
Now add the outside terms and multiply it to the inside term (The terms inside the
parentheses should be the same in each part of the problem.
(2d-5) (5d-4) Answer
Practice Problems
By Jamari Robinson
2
10x +21x-10 12q2+34q-28
8z2+20z-48
12y2-4y-5
Adding and Subtracting
Polynomials
Example
:
Problem
1
2
2
2
(30x

10
x

8
)

(
10
x

20
x

4
)

40
x

30
x

12
2
2
2
2
Guid
:
30x

10
x

40
x
/
10

20

30
8

4

12
4

3
x

/
1
When adding polynomials you must find all like terms for each variable, exponent and co-efficient and you must add
them with each one that is the same term.
Example
:
Example
:
2
2
(
60
x

12
x

3
)
(
30
x

2
x

1
)
2
2
(
20
x

10
x

2
)

(
10
x

20
x

1
)
Subtraction for polynomials wouldn’t be too different you would just find the variables, the exponents and the coefficient and instead of adding you would subtract.
-William Higgins
Example
:
2
2
(
20
x

10
x

2
)
(
10
x

5
x

1
)
Example
:
2
2
(50x

20
x

5
)

(
14
x

10
x

5
)
Solving equations with multi step.
I am going to talk about how to solve multi step equation as you can this
equation below is a multi step equation. It contain coefficient and one variable
and distribute to clear the properties
4(50  3x)  80  20
200  12x  80  20 Distribute the parentheses
Practice
200  12x  100 Simplify the equation
problems
3(3x5)49
 12x   100 Subtract both sides
3x519
x62
12x
 100 Divide both sides


x4010347
12
 12
2(910
x)3040
you divide them
x  8 . 3 3 After
you get the answer.
Guervens Charles
Finding the equation of a line given two points
Description
To be able to solve this
concept, there is two things
that you need to know. First
thing you need to know is
how to find the slope of a
line using two points. The
second thing you need to
know is how to find the yintercept of a line using two
points.
4 practice problems
(-2,0) (8,4)
(-3,0) (3,3)
(2,4) (4,8)
(8,16) (16, 32)
Example
• (-1,0) (1,4)
• Find the slope
Slope=
• Slope= 40 4
 2
1


1 2
y2  y1
x2  x1
• Find the y-intercept
• You have to solve for b (y-intercept)
• Let (1,4) be x and y
y  mx  b
4  2(1)  b Replace the letters by their values
4  2  b Multiply the slope and the x value
- 2 - 2 Minus two on both sides
2  b The answer is 2.
• The equation is y=2x+2
Rubens Lacouture
Multiplying A Binomial By A Binomial
Kasie Okafor
(
x

3
)(
x

2
)

x

x

x

2

3

x

3

2
Add The Result:
x

x

x

2

3

x

3

2
2
x

2
x
3
x
6
2
x

5
x
6
(
m

4
)(
m

5
)
(
y

2
)(
y

8
)
(
x

5
)(
x

7
)
(
x

3
)(
x

4
)
The Answer
Solving Inequalities using all operations
Description:
An Inequalities
is the condition
of being
unequal lack of
equality
disparity.
3 x  9  6 x  12
 3x
- 3x
9  3x - 12
 12
4 Practice Problems:
2x+ 6 > 4x- 16
9x -5 < 45x +12
8x-9>7x+12
8x-5<23x+13
x
 12
21
3x

3
3
7  x
First you -3x to
both sides ,
then you have
9>3x-12 you
have to +12 to
both sides.
Then you have
21\3 >3x\3
you cross 3x\3
out and 7> x .
Your answer
x>7.
 7
Jennifer Jean-Louis
Multiplying polynomials
A trinomial has three terms
and a binomial has two
terms, but they are all
polynomials. To multiply
polynomials you have to
multiply each term to every
other term. An example of
this is:
3
(
x

2

8
)(
4
x

8

2
)
Step 1:
To do this problem, you have to
take the first term which is x cubed,
and multiply that by all the other
terms in the trinomial next to it.
(4x+8+2) You have to continue to
do this with each term in the first
trinomial. Once you do this, you
will get this for the answer. You get
this by combining all the like terms.
33
34
3
3
x

4
x

x

8

x

2

4
x

8
x

2
x
Step 2:
2

4
x

2

8

2

2

8
x

16

4 4 Practice Problems:
2
2
(
7
x
x
3
)(
7

8
)(
3
x

1
)(
x

2
)
Step 3:
8

4
x

8

8

8

2

32
x

64

16
5
x
(
x

3
)
4
x
(
x

3

8
)
2
Answer:
3 4
10
x

4
x

40
x

100
Mykala Jordan
3x4y 25
2x3y 6
Multiply
by2.
6x8y-50
Multiply
by-3. ()-6x9y-18
17y
-68 Add
theequations.
17y -68

Divide
each
side
by17.
17 17
y-4 Simplify.
Now
Substitute
-4foryineither
equation
ofind
t out the
value
of x.
2x-3y6
Second
Equation
1
a
.)5x3y6
2x-3(-4)
6 y-4
2x5y10
2x126 Simplify.
2x12-126-12 Substract
12from
each
side.
2x-6
Simplify.
2x -6

2
2
x
-3
3c.)
6x
-2y
10
Divide
each
side
by2and
Simplify. 3x
-7y
-19
The
solution
is(-3,-4)
2b.)
6a
2b
2
4a
3b
8
4d.)
9p
q13
3p
2q
-4
By: Mark Britt
Distributive property to simplify and
solve expressions.
one
way
is
th
pr
at
12x(4y
oblem
th

2x)
eth
you
an
12x
an
take
d
multiply
by
4y
an
th
den
th
12
an
multiply
e
take
d
it
by
2x
you
2
distr
d
th
pr
ibute
e
12x
oblem.

4y

48xy
an
12x

2x
d

24x
th e
12
x
(4
y
2
x
) an
is
48xy
swer

24x
.
(
12
x
4
y
)
(
12
x
2
x
)
48
xy

24
x
2
expression
A mathematical equation which can contain
numbers, operators the four operation and
variable (like x, y) to represent equation or a
operation. Like 12x(4y+2x)
5 x  5  15
Solving multi-step equations
with
 5  5
Practice problems
operations
7m17
60 5 x  10
/ Description,
5  /5
Practice problems
5
x

5

15 examples
x 2
all
1. To solve the
7
x

4


32
2.Then divide 5 to 5x,
problem above, you and 10, and you will
subtract 5 from both get x=2. The variable
sides.
is 2.
3
b

4

13
•
Multi-step equations are equations
that takes more than 1 steps to
solve that specific equation. Such
as some examples below. They just
basically requires more work.
Here are some examples
8

3
r

7
2
a

6

4
Jackson C.
Ngo
Finding the equation of a
line given two points
Use
the
following
coordina
s,
practi
to
find
th
eq
1.
(6,1)
(8,3)
2.
(6,
1)
(9,0)
3.
(5,10)
(10,15)
4.
(7,21)
(8,24
Tofind theequationof a linegivenby twopoints,youuse twocoodinates
tofind theslope,
andfind they - interceptbyseeingwherethelinecrossesin thegraph,
or pluggingthecoordinate
to theequationyoufound.
Tofind theslope,youusetheequation,
2
1
2
1
y y
x x
in someequationswherea gridis available,
youcanusetherise/runmethodtoalsofind theslope,
they is therise thexis therun.
Wewillbeusingthecoordinate
s, (1,2)and(4,5).
2
2
(4,5)
1
1
Coordinate
(4,5)wouldbe y andx whileCoordinate
(1,2)wouldbe y andx
(1,2)
5- 2 3
 Yourslopewouldbe3 because
3 dividedby1equals3.
2 -1 1
Theformof theequation ewwantis y  mx b (bbeingthey intercept,
m beingtheslope)
Soyourequation ould
w bey  3x b.
Tofind they - intercept,
you would
substitute
a coordinate
, into thecurrentequation.
So,y  3x b usingthecoordinate
(4,5)it becomes
, 5  34  b , 5 12 b
12- 5  7 , therefor
youry intercept
is 7.
y  3x -7
By: Junior Tatis
Multiplying a Polynomials by a Monomials
Polynomials are just two or
more monomials added
together. When an degree is
asked for a polynomial its
usually asking for the
highest exponent for a
variable.
Examples:
(p3)(p24p2)
p(p2)p(4p)p(2)3(p2)
In order to do all these you
would have had to had
known distributive property
p35p2p3p2
p33p3p2
2
(
x

2
)(
x

2
x

1
)
2
2
x
(
x
)
x
(
2
x
)
x
(
1
)
2
(
x
)
2
(
2
x
)
2
(
1
)
Try these, real fun!
(2x 2)(x2  2x 1)
(4x 1)(x2 4x)
(4x 2)(x 4x 2)
(3x 3)(x5 9)
3
2
2
x

2
x

x

2
x

4
x

2
3
x

3
x

2
Practicing will prepare you for success
on the Math Finals!
Tatyana Adams
Solving Systems of equations using
4 Practice
substitution
problems
Example
x  2 y   21
2x  7 y  3
x  1  4 y
x  2 y   21
x  2 ( 3 x )   21
x  3 y  12
x  y  8
y  3x
x  6 x   21
7x   21
x  3
y  3x
Simplify, Combine the like terms
Divide each side 7
Use y  3x to find the value of y
y  3x
y  3(-3) or - 9
The solution is (-3,-9)
Check the solution by graphing or
put the solution in the problem to see if it makes sense
6x  2 y  4
y  3x  2
a  b  1
5a  3b  1
Description:
Use the
substitution
method to
eliminate one of
the variables in
your equation.
When you find
the answer to
one of the
variables plug it in
the equation to
find the other
variable.
Nedcar Faugas
is an algebra property which is used to multiply a single term and two or more
terms inside a set of parentheses. Take a look at the problem below.
example2
3
(
x

x

1
)
2
2
3
(
x

x

1
)
3
(
x
)
3
(
x
)
3
(
1
)
2

3
x

3
x

3
Practice these four-
1( x 2  x)
3( x  2  x 4 )
7( x  x)
4(3  x 2  x  2)
Solving Inequalities Using All Operations
10
n

63

4
n

27
A
multi
step
equa
10n

63

4n

27
First
step
isto
get variable
the
by
itself

4n 
4n Subtract
he
like
variables
t
6
n

63

27 Then
you
add
the
terms
EXAMPLES

63

63
6
n

90
Simplify
and
divide
by
six
66
n

15
Solving Inequalities using all operations is when
you use all the steps and operations you learned to
solve inequalities. You need to know how to add
and subtract like terms. Also you would need to
know how to simplify equations. You will also
need to graph them on a number line.
2n20 4n32
6x12 2x 64
9v 183v21
10g 505g 25
Karan Richards
Multiplying a Polynomial by a Monomial
2
2

2
x
(
3
x

7
x

10
)
Dis
Us
ve
Pr
2x2(3x27x10
)
2
2x2(3x2) (
2x2)(
7x) (-2x
)(
10
) - Distribute
the
Polynomial
to
each
ofthe
Monomials
in the
parenthesi
s.
3
6x4(
14x
) (
20
x2) - After
you
distribute
the
Polynomial
to
the
Monomials
make
sure
that
your
multiplica
tions
are
correct.
Make
sure
that
your
exponents
are
correct
and
that
your
negatives
and
positives
are
in the
right
places.
6x4 14
x3 20
x2 -
Multiply
he
new
Polynomial
t
by the
Monomials
in the
parenthesi
s
( Use
distributi
ve
property
!!!!!!!)And
make
sure
you
have
the
correct
exponents
and
that
your
negatives
and
positives
are
in the
right
place
and
Ifyou
did
your
multiplica
tions
correct,
you
should
have
your
answer
:)
Try some for yourself :D
2
2
23
2 2
2
5
a
(

4
a

2
a

7)
5y(

2y

7
y
)
6x
(
5

3
x

11
x
)

4
x
(
5
x

1
x

7
y
)
To solve this equation you need to use the distributive
property. Distribute the Polynomial to all the
Monomials in the parenthesis.
Yanick Cardoso
DIVIDING MONOMIALS
•First take the 12 and divide it by the three. 12 divided by 3 is 4.
•Then were going to take the a’s from up top, and at the bottom
and see how many pairs we can cross out.
We crossed out 3 pairs so at that
point. Now it’s a raised to the 3rd
power. So now were going to do
the same to the next variable
which is C.
9 12
12a c
3 6
4a c
aaaaaaaaa
aaa
Practice Problems
5
4
3
4
7
10 s
5s3
25 g
6
5g
10 13
30y f
6 6
5y f
10
ccccccccc
cc
cccccc
We crossed out 6 pairs so that is going
to be C raised to the 6th power. At the
end your answer should look like this.
3 6
4ac
Jhlyik Lezama
Multiplying a polynomial by a
monomial
We are going to do “multiplying a
polynomial by a monomial”.
Where we multiply whatever is in
the parenthesis with the outside
variable.
Our first step is to multiply both
Here is our
variables inside the parenthesis with
example
the outside parenthesis
8(2x -6)
After multiplying it would give us our
8(2x) 8(-6) final answer of 16x – 48
16x - 48 With that you are done and free to
try some practice problems below.
4 (6 x  8)
9 (5 x  3)
8(4 x  8)
6 (6 x  4 )
Vu
Nguyen.
Multiplying a polynomial by a monomial.

2
x
(
3
x

7
x

10
)
22
First thing is the distributive property.
2
2 2
2

2
x
(
3
x
)

(

2
x
)(
7
x
)

(

2
x
)
1
)
The next thing is to multiply

6
x

(

14
x
)

(

2
x
)
4
Examples:
3y(5y2)
2x(4a4 3ax
6x2)
t(5t 9)2t
3
2
After you multiplied you have to simply
4
3
2

6
x

14
x

2
x
4xy
(5x2 12
xy7y2)
Brittany Odom 
Solving System of Equation Using Substitution
When you Solving System
of equation using substitution
you have to solve for “y” and
“x”. Because solving system of
equation you know you have to
Practice Problem I
find two solution.
Example I
Solve for x
 y  4x  2
6 x  1y  4
6 x  1( 4 x  2)  4
6x  4x  2  4
2x  2  4
2x  2
x 1
Substitute y=4x-2 into the 1y
Distribute Multiplication
Subtract 6x-4x
Add 2 both side
Divide both side by 2
Solve for Y
y  4x - 2 Sub the X answer from the previous Problem
y  4(1) - 2 Multiplication
y  4-2
y2
Answer is (1,2)
3 y  2 x  11
y  9  2x
Practice Problem II
y  3x  2
8x  2 y  4
Subtract 4-2 to find Y
Fredens Altine
Solving Systems Of
Equations Using
Substitution
Steps to Solve Systems by Substitution
• Solve one of the equations for y
•Substitute the expression for y into the
other equation.
•Solve for x.
•Substitute the value of x into either of the
original equations to find the value of y
•Write the solution as a coordinate pair.
x - 2y = 14
x + 3y = 9
a. First, be sure that the
variables are "lined up" under one
another. In this problem, they
are already "lined up".
b. Decide which variable ("x" or
"y") will be easier to eliminate. In
order to eliminate a variable, the
numbers in front of them (the
coefficients) must be the same or
negatives of one another. Looks
like "x" is the easier variable to
eliminate in this problem since
the x's already have the same
coefficients.
c. Now, in this problem we need
to subtract to eliminate the "x"
variable. Subtract ALL of the sets
of lined up terms.
(Remember: when you subtract
signed numbers, you change the
signs and follow the rules for
adding signed numbers.)
d. Solve this simple equation.
Try these ..
e. Plug "y = -1" into either of the
ORIGINAL equations to get the
value for "x".
•4x + 3y = -1
5x + 4y = 1
f. Check: substitute x = 12 and y
= -1 into BOTH ORIGINAL
equations. If these answers are
correct, BOTH equations will be
TRUE!
•4x - y = 10
2x = 12 - 3y
•x - 2y = 14
x + 3y = 9
P = 2 + 2Q
P = 10 – 6Q
x - 2y = 14
x + 3y = 9
x - 2y = 14
x + 3y = 9
x - 2y = 14
-x - 3y = - 9
- 5y = 5
-5y = 5
y = -1
x - 2y = 14
x - 2(-1) = 14
x + 2 = 14
x = 12
x - 2y = 14
12 - 2(-1) = 14
12 + 2 = 14
14 = 14 (check!)
x + 3y = 9
12 + 3(-1) = 9
12 - 3 = 9
9 = 9 (check!)
SHAY
WEBSTER
Adding and Subtracting
polynomials
When you are adding/subtracting polynomials, you have to add/subtract like
terms.
When you are done adding like terms you have to put them in order from largest
to smallest, answers with exponents always go first.
EXAMPLES! 
1. (2x+3y)+(4x+9y)
{add the x’s first then the y’s}
6x+12y
Practice problems for you to
try…. 
• (5+4n+2m)+(-6m-8)
•(5a+9b)-(2a+4b)
•(5f+g-2)+(-2f+3)
•(11m-7n)-(2m+6n)
2. (6s+5t)+(4t+8s)
{add the s’s first then the t’s}
14s+9t
Jonique Tabb
Solving Two Step Equations
One goal in solving an equation is to have only variables on one side of the equal sign and numbers
on the other side of the equal sign. The other goal is to have the number in front of the variable
equal to one. The variable does not always have to be x. These equations can make use of any letter
as a variable.
1. 3x+10=100
3x+10=100
2. 7x+10=52
Were basically going to undo the probably
by doing the opposite. So first I’m going to
subtract 10 from both sides. That’s going to
leave me with 3x=90.
-10 -10
3x=90
_ _
3 3
X=30
Then were going to divide both sides by 3.
3x divided by 3 leaves you with x, and 90
divided by three leaves you with 30. Your
problem should be finished off with x
equaling something which is 30 so x=30.
7x+10=52
-10 -10
7x=42
_ _
7
Subtract 10 from both
sides.
Divide both sides by 7
7
X=6
There’s your answer
Practice Problems
1. 3x+5=14
2. 2x - 3=-9
3. 3x-2=10
4. 3x+5=14
Cookie Bourne
Factoring Trinomials
Factoring a trinomials
means finding two
binomials that when
multiplied together It
makes a trinomial. This
is kind of like the
opposite of multiplying
two binomials.
1x²-10n+25
1x²+15n+14
1x²-8n-48
1x²+p-20
EXAMPLE
1x² + 5x – 36=
(x + 9) * (x – 4)
SOLUTION
The problem asks me to factor the
trinomial into two binomials.
STEP 1
List out all the factor of the number
with no variable.
STEP 2
Add/Subtract the factors of that
number and see if it adds up to the
middle number.
STEP 3
After that turn them into two
binomials.
Jimmy Lai
Graphing the Solution of an inequality on a
number line
EXAMPLE:
Graphing inequalities on
number line represent the
solution to inequalities . It aids
in visualizing the answer.
Graphing inequalities is simple
once you learn the few simple
steps to solve a problem.
PRACTICE PROBLEMS
Graph: x < 4
Solution: The problem asks you to graph
all numbers that are less than 4.
STEP1: Draw an open circle on the
number 4. (Don’t draw a CLOSED circle
because it does have the _ under the
symbol.
STEP2: Draw a line going left, because x is
less then 4.
HERES THE SOLUTION
X<-9
x > 24
| 2x + 3 | < 6
5 >x
Parmanand
Jodhan
Multiplying A Binomial By A Binomial
My project is to
multiplying a binomial by
a binomial. When you
multiply a binomial by a
binomial you have to
multiply every number in
the problem by each
other.
Practice problems
(6 – 2x) (10 – 7x)
(12x + 4) (3x + 7)
(8x – 9) (14x – 13)
(9x+ 24) (5x + 1)
First you do 3x times 5x and
get 15x. Next you do 2
times 4 and you get 8.after
that its 2 times 5x the
answer is 10x.lastly you do
3x times 4 and it equals
12x.
Alisha Cooper