Date: _ _ __
Algebraic Expressions - Simplifying Algebraic Expressions
2~) +l"{fx)l)
(-3.Sx+ 1.7) + (9.lx+--0.3)
Zx ·H; +- 3x .J-1
-3.5x+ Q.I x)
(~t.~;) +(!?l-))
II
Sheet # 04-06
PreAlgebra
+( 1. t +-.3
~~
rs~~~+-+r v
---........
.....-.'
~
-~
I (2x-t--5) H(3x-V4)
2x +-5 f- - 3>C +4
(2 x + -3x) + ( -5 +4)
-1 x
o~
-1- -1
-;)
C: :x ::l_]
S(It?4) + (2x t7)
-zo + 2.X 4 -1
rsx + 2 x) + (- l 0 -I )
5x+
+x
h+~;~~
-2~
(-2x-4)-
x
-zx+-~+ -21'
(-2x + -2x} + ( -Ln
-4 x + -4
otH{"![)
(7x+2)-mx+3)
1x+;; + 3 x +-3
(+x+3)()
+ (2 .i- -3)
I 0 X' + -ir
- ) +(4.9xtl.4
_r:..~ )
(5.7xt--:0.8
5.t-x+-., R+- -1~9x+ I ,,4
{ S., =t x + -f. 9x) +( -., 8 +- l. ~)
~
l~s)t2x
5
(6ab + 2a + b) + (3a-l--2b)
0ab +Ja-rh +3a +-2b
~0-b +(Ja +3°') +(b+ -2b)
Gab f- 5a + -b
~~12-±.sa;D
~t(c + 2d)from Be -3d)
X+ -3 +--ix
(x+-1x)+-3
-x +-3
<~72J
t4c+3d) +(ct 2d)
4c+-3 d + -c + - 2J
f4c +-c)+(:..3d ~ -2d::::;...,~
3 C -1- - 5 d or· , c - 5d
What is the additive inverse
of 8 ?
qJpDsrte .s'~n
-8
Uii?>
~
5(xf3)t"x
5x +-is+- -x
(5x + - X ) .J-- ( -I\ )
4x +-1r
What is the additive inverse
of 5 x - 8 ?
opp o<:.i*te- _9&f't
-5x+8
~-
~
2(x+1)+3x
Jx+J~-3x
{Jx-1- -3x) + 2
-1x
+2.
~
What is the additive inverse
of-5x-8?
5X+8'
~()-~
SF~(hf3±)
g+- --j r +14
j r i' +14)
}=}r f~
-1- (
--
PART A
Find the difference. (9 p fl 5) t (2 p + 3)
A 7p-12
t -1 +- - 2 p+
7p-18
c llp-12
4· ~ p )
D llp-18
qp
( qp
®
A square has side length x - 2. Find the
perimeter in terms of x in two ways.
'l-2
s
+( · Kf
3)
1p-+ -/~
~-\
X-2
Ofl.
Choose a value for p and substitute it into the
expressions to prove your answer is correct and the
other choices are incorrect. Le. f p .: : 2
A
(qpc-15)-( 2pt3)
(q·;)-JS)-(2"2·f3)
I
r·
:3J ____
't~~~ll~
[I]
i-~J
____
•,
An equilateral triangle has side length x - 2.
Find the perimeter in terms of x in two ways.
~
f-y
9-/t ---
~~----
v
x-2
(5x-3)-(7x-10)
Steps
Property
(5x-3)-(7x-10)
given
.
.
1
- _acL_J_i".:i_+ttt
_,.L_··lr_~1~c~l'1~J;•~i~
Ml/fl' Se
_<,_·,
5x t ~3 + -1 x .f- ID 1),s~ bu hve fvupe_.,..f·-y
5x1 -1x + -3 +JO l~1rviMu:fa~ve
-Jx
x
+ -3 +to)
l\k 1 "oo 1_
I
! Mint oD 2
I
(XtX+x)+(2·hH-2
3n--=·2)
3x +-b
(/3~~~
~)
Show the steps to simplify the followin~
expressions and justify each step with the property
used. [There may be more lines than needed]
(5 ){ f -
~.·-·---~
fZTl
, (Ifil
(5 x+ _3\l + _-,f-r__,+-i'll
(-'"'
-~-2 ,~
/ .......
I
Ttp-= 12 \-II p~!(
~11::2-12 \ 2-·1t
11
4 (X ·-2.)
<!BJ
___]__
11.rll~
x +x -I.· x __+,/\-+(-2+-2+·i
~J
x{ _____ ('-2 §fl
PARTB
Jl t~19111c I
(
_ , A ___ - ,
H5S ~oc five
+ 1-
Mei plans to trim a picture tq fit the ength of a
frame. The plcture isQ2x + 4)units long, but
the frame is only(7x + l)mits long. How many
units of the picture will Mei have to trim so
,,that is will fit ii:to the fra?'le?
S b h'-ccf(J 2 x f t/) - (
x. ·f , )
Lt
( 1
x+l-n
+T ;i K
f
i)
) 141- )<f ,
(I Jx +- 1- xl-1(4 +·-·1)
(
/~X'':i'
:!:.~l~J
J
.
FIND THE ERROR
Arianna is finding (5x+3)-(2x+l). Find her
Find the perimeter of quadrilateral ABCD in
terms of x. Write the answer in standard
form.
,
A_~' (J~-~~x)+(si-2)
3x-2
D
3x
c
[not drawn to scale]
{qx+31
Name: _A__;n..:.,.,..s.....,;_we_{_fiR__._4_ _ _ __
Date: _ _ __
Algebraic Expressions Directions:
PreAlgebra
Simplifying Algebraic Expressions
Sheet # 04-07
~ ~ ~
~
Part 1: Simplify each of the following expressions. Determine which expressions are equivalent to 5x -15, 5x + 15, - 5x + 15, or'_ 5x -15.
Part 2: Choose a value for x. Evaluate each expression to check your simplification.
lJ>e. x:: 1-
f\I Skill Level 1
5Cx - 3)
~
Ll5e X:: :)
5{;i-3)
@/
Skill Level 2
2x+10-7x+5
Skill Level 4
-
2x+3N
[J x +-(-+~}]+uo + 5]
c\uc~
[J-x +- 3 0-15
d"d+ 3(;) -5"J
-5 /
~
~
~ .d-)(<
k\\) -1'
';}_"';)_
((\
5(x + 3)
-;/
0)
2x-10-7x-5
-(25x-75)
5
§
~
ti!
("< ,;;;..-:f'>
I
~ .?·
.-5./
3x -t 5 +J :x -+ \ \J
+d )<J +0 .\ '~J
Dx
~~
~--~
¥-
l1
<;; x + (-Ix~+-/} 5 + (- 'IJ
-~
~~
~
cite.ell
~
-5(2-i-3')
- z_<; ./
3x + 10 + 2x - 25
[3x +:1 x J +!]o -t- (:is)]
. .--7
v
Sx _,. -1t;
,,,M-~·~--~
~
-3x-J5 -2x
(.3x +(-1x~+-(-1\)
-5x-+ -1<;" c~ . . -:>..;r
~
:)><=K
- ~(>'~'
-isv
~
3(x + 4)- (8x -3)
3X+ld -~X
.
~~ -i(?...>r
cv~ is./
y::\\
-3(x + 5)-2x
~
~
cY\JLC~
-
-5(x-3)
·-~)
~
(3x + 5) + 2( x + 5)
+3
[Jx+ c-~~ +Gd-t 3]
C5X-r1D~
3(H~);~-;)
Justify each step of the simplification with the
property used.
The number of questions on a math test is
represented by (3x + 1). The number of
questions on a spelling test is represented by
(x+12).
(5x-3)-(7x-10)
Steps
Property
.
given
(5x-3)-(7x-10)
d1s~1bu~ve ptop.
5x-3-7x+ 10
5x+(-3)+(-7x)+10
5x+(-7x)+10+(-3)
[sx + (-7x)]+ [10 + (-3)]
St.Jhfrtlc'hc:id\ I.)
a.de~•~ fk..
1~·hJei5.e
Com~ ufcbve "'f?0:.p
/1s<;h(lt-hve ,...Pib9.
If P = a 2 +a -1 and R = -a -1 , which
expression represents P + R ?
2
@:::~
D
~
/
\_3x+I) -(x-t· 12)
5x+I -
(o +a-/)+ (a-11
aa. tb.-~..J-{ii)j +(-1)t(1)
a 2 + 2a
aZ. + _2
2
a + 2a - 2
The table shows the breakdown of points scored
in last week's basketball game.
x-12
(3x +(-I ;·)·f+[i
+(-12)]
.:.;
'....-..
combine
-2x+7
c
PART A Write an expression to find~
~questions were on the math test. St.it hIv.. <j-
;J >< -JI
<9x+-JI
questions
PART B Evaluate the expression is the value of
xis 8.
;<;x. -11
d"8 ~-11
IC - If
5
- - - - - questions
5
Rectangle LMNP is shown below.
L
3x
+ S meters
M
4x - 3
4x-.3
meters
p'--------'N
PART A Write a linear expression in simplest form to
represent the total points scored in the first two
quarters.
2{x-J)t
.J><+ x +-
.,t.
(··h)
3x-4
_ _ _ _ _ points
PART B Write a linear expression in simplest form to
represent the tot~ scored in the game.
3 X -4 + ~(x+ 5~)-2x +·Cf
-' x · ti ·f 2x +I oo - 2 x + q
. X +*->t-4-{~)] f{~f-9 +(~'f)J .J7X:1(0~oints
3X+I05
Part C If the value of x is 3, what are the total points
earned in all four quarters?
(O \
q1- J05
LMNP?
?Jdd afl 5 t cl~ 'i
~
4x-i fx)+C 5-1·5 + l··3)+{-;d]
/A7Xf 711
11'<+1
meters
Emma and Aailyah simplify the same expression, as
shown below.
Emma: -5x + (2 + x) = -5x + x + 2 = -4x + 2 V
Aail'.ah: ~5x
+
(2
+ x)
= :-~(._·fro~ t xt= -: ~ x
Who s1mphfied the express10n correctl}J +e
!:.
c!) Only Emma
B Only Aailyah
C Both Emma and Aailyah
D Neither Emma nor Aailyah
Wl;U_ch of the f~ing expressions is equivalent to
- n(2- k) + n(k-'2)?
-2n -1- nk +-nl< -2n
3x:+10~
3·3 .,.,
What is th~me§Din meters, of rectangle
Gx+ 3x -1
X·fl
2.x-t;..+x1·2
3x+ s
_)_)_~_ _ points
-2n+(.2,..,) .}ri)(+\\'K.
- 4 n + 20 K
,AC' o
,..w
-1
A
-4Yr\
2iz(k- '2)
2<'lK -L}()
\£)
Ans vvel Kn.4
Name:
Date: _ _ _ __
Algebraic Expressions - Factoring Linear Expressions
Find the greatest common factor (GCF) of
each pair of monomials.
Part A Factor each expression. If the expression
cannot be factored, write cannot be factored.
Part B Simplify your answer in part A to check.
•. I[};:__....dJ..
(a)
4x
2()..,
(b)
J8a,20ab
(c)
12cd, 36cd
(d)
12,28c
3
r- /21 11
3)63;,8~ ._21_
(g)
4x, 12.x - -
,
(i)
j_
(j)
Sx
(k)
:t fYl (}
(l)
"'1-
·",;_LL........ l'J.....
(h)
12cd
G
..................# ..... ~
"
:t )30rs,
42rs _ _
(5
60jk, 45jkm
Sheet # 04-08
PreAlgebra
J
PART A
PARTB
~)
(a) 3x+9
3
5j r
3x f q
v
l
(e)
25x, 15xy
(f)
42mn, 14mn
(b) 12x+ 7y
lOOxy, 75xyz /25x~
Which pair of monomials has a GCF of 4a?
~ i6a, 811 8 gf'f
~ 16ab, 12b nof a..
1
(9}
~ 18a, 8a
l6ab, 12a
(c) 4x-28
4
The Venn diagram shows the factors of
12and18x.
l2
4
\
4x
)
1Sx
3( x +lh/)
3x + 33 y /
(d) 3x+331!
3
3 (x+lly)
What is the greatest common factor of the
two monomials?
A
B
©6
2
3
D
36
Which of the following expressions cannot be
factored?
A 6+3x
c l5x+ 10
\!!) 7x+3
D
30x+40
Oo-f~,oa
1/l Co"'l"I "'1"!
J
--
Explain how the GCF is used to factor an
expression. Use the term Distributive Property
in your response.
'
t
. :
Ca r1llot he %tiiDrad
1
(e) 4x+35
(f) _]_6x_± 2_4
12-
/)
rxJ.·'
I()
·7J
..:;. ,.,..
~---~
(g) 14x-16y
1
;--;P'-
2(=t7--gy)
J.fx -16 tf
v
The drawing of the garden at the right has a
total area of (15x + 18) square feet. Find
possible dimensions of the garden.
. FIND THE ERROR
Rodney is factoring 90x -15 . Find his mistake
and correct it.
)5x+I~
3
3 (5X4h)
Write an expression in factored form to
represent the total area of each rectangle.
A.
5
49x
?o
5 { X.f 4)
18
)(
6x
Write an expression in factored form that is
equivalent to the given expression.
Expression
+( I +1 X)
(d) 5
1
-x+4
-x-30
6
2
I
20x
40
(b) 2
-x+6
__J
_______
12
Expression
(a)
1?:..__q __ 5-.25 . . T LO
(:;
3
2.
4m
c.
7
5x
Expression
B.
4
x
Write two monomials whose greatest commonfactor is 4m.
Gff+ x)
Expression
:1/3
)
\f\J : "f
J. :
X -.2
. , w, x -2
u~j
4
The area of a rectangular porch is
(9x + 18) square units. Factor 9x + 18 to find
possible dimensions of the porch.
q(xt2)
w· q
j· q
£·';(+2 o'- N'X12
Six friends visited a museum to see the new
holograms exhibit. The group paid for
admission to the museum and $12 for parking.
The total cost of the visit can be represented
by the expression $6x + $12. What was the
cost of the visit for one person?
G<x+l)
@
. -3
~
(c)
-x+16
5
~
Gi
f( x
(f)
3
-x-24
4
~
-f(x-
(e) 2
,,{;..
f(x+q)
The area of a rectangular dance floor is
(4x-8 )square units. Factor 4x -8 to find
possible dimensions of the dance floor.
4(x -2\
G- ·x
J1.f;.1_
'+
-3
4 .. 4
.,::.
0
2)
Hi-2
z
lb .. _s:
2.
r4-0)
3
-x+18
8
%
(x ~ft)
1&~.1'i?
(,
1--'l' * '<
8'
~-4
Name:
ArlS\.Oetl
Algebraic Expressions - Mixed Practice
State whether the example given illustrates the
associative property (A), commutative
property (C), or the distributive property (D).
C
(a) x+9=9+x
A
(b).1oo+c52+45)=ooo+52)+45
~
~
Date:
in the expression: 4x 3 - 2x 2 + x -5
4
4x 3
1
Coefficients:
f\\
Sheet# 04-
Identify the terms, coefficients, and constants
Terms:
(c) 2( 5 + 3) = 2(5) + 2(3)
-----
PreAlgebra
r1
Constants:
-
-;lx
-
J
7
1
-?f
2
-fr
5
~~~~~~~~~~~~~-
Which of the following expressions cannot be
factored?
A
6+3x
c 15x + 10
@) 7x+3
D
30x+40
A Web site charges $0.99 to download a game
and a $12.49 membership fee.
Part A Write an expression that gives the total cost in
dollars to download any number of games.
The cost of a game g with a 7% sales tax can
be represented by the expression g + .07 g .
PART A Determine the cost of the game after sales
tax if the game costs $52.
g+ . o:r9
Algebraic expression:
"
q q9 + I '.L 4q
Part B Find the cost of downloading 6 games.
.99(ra)+l2~'-f.q
.
5~-1- ~D".1{52) ~
Answer $_/_K.~1~3
___
5;; ~ 3-fo"
PART B Simplify the~+ .07 g .
/.f./J1
~
PART C Use the simplified expression to find the cost
after sales tax of a $52 game. / _o ~ .9.· ~
l
():j(\ l)
@!!V
Tonya has x quarters (worth $.25 each), y
dimes (worth $.10 each), and z nickels (worth
$.05 each), in her pocket.
Part A
Write an expression to give the total amount of change
she has in her pocket.
Expression:
1
;J 5 X + ·I() l/ + .o ~ .:c
= -64.
t/o@'-1) C) 26
+
@ 154
Evaluate 90 - k when k
A)
B)
164
36
Evaluate a2 - (a 2 - b 2) when a
b=3. (-2)2.-((-2\
A)
@
1
9
2
= -2 and
-3;i.)
C)
D)
-9
-1
+
Whicj:l expression is equal to "13 ~the
guotienl of n and 8"?
C
nx8+13 J3+ ()..'.
A 13n..,..8
B n-8+13@ n..;-8+13
·
PartB
Tonya has 5 quarters, 3 nickels, and 2 dimes in her
pocket. Use your expression above to determine the
change Tonya has in total.
, 25((') .10(.l) .o~())
+
+
Total change worth$ _)_,-"'0-C;.O_ _ _ __
- Which expression is equal to "five~ a
number multiplied by 3"?
~
A 3(x- 5)
C
5 - 3x
/l _
3
5
B Sx - 3
@ 3x - 5
'I
g
The drawing of the garden at the right has a
total area of (1Sx+18) square feet. Find
possible dimensions of the garden.
FIND THE ERROR
Rodney is factoring 90x -15 . Find his mistake
and correct it.
?o y--1 s··
!5x+IB
_.:..--;---
----i~-----
;!
5( 6x - J)
J
The charges for a large pizza and each topping
for two pizzerias are shown.
l
-
t
I Mailh1$".Rl2la i
10
IPlziai:§il~ia:ce !
12
i
I
1.50
i /J +I. (0-1::
Write a linear expression that represents(flQ~~tr- t
~~a pizza with t toppings would cost at Pizza IJ
'
Pafue than at Mario's Pizza.
(id .f I. 5 f) - (Io ff. 7r.; t)
}d +/, St - I 0 - J Afg~b~c expression:
J_ +•dS ../:;
Pamela wants to attach a string of lights to the
edges of her patio for a party. She does not
want the string to go across the edge with the
steps.
4x-2
(a) (-2x-4)-(2x)
-Jx- 4 -:Jx
G~
(b) 5(x-4)+(2x-7)
5x -2 o + 2x - =t
~
(c) (7x+2)-(-3x+3)
-::fx.+d. +·Jx
4x-2
~
x
3x
Write a linear expression to represent the
length of string in feet she will need.
4x +fx. 13x .+x
I Jx
- J.
+ -2
(d) (3x-2)-2(x+4)
3 .X - ;)
- 2x - g
~
-4
Expression _!_2_X_,,..._4_·__
1
(e) S(x-3)-x
5x-/)-X
Find the length of string if x = 3.
J~
Cf0J:>
x -4
3 -4
J:,-4
);) 0
Length:
(f) 2(x+l)-3x
:J..
I
Express each algebraic expression in simplest
form.
lo+ /.25-t:;
1.25
~!~-·~·-+-·~--+~~~~
~-
2.X-+ '),.
~