Download Solve One Step Equations - Killingly Public Schools

3OLVE /NE3TEP %QUATIONS
'OAL + 3OLVE ONESTEP EQUATIONS USING ALGEBRA
9OUR .OTES
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%QUIVALENT EQUATIONS ʵÕ>̈œ˜ÃÊ̅>Ìʅ>ÛiÊ̅iÊÃ>“iÊ
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7ORDS
!DDING THE SAME NUMBER TO EACH SIDE OF AN
EQUATION PRODUCES AN Ê iµÕˆÛ>i˜ÌÊiµÕ>̈œ˜Ê !LGEBRA )F X A B THEN X A A Ê LÊ Ê >Ê
OR X Ê LÊ Ê >Ê 35"42!#4)/. 02/0%249 /& %15!,)49
7ORDS
3UBTRACTING THE SAME NUMBER FROM EACH SIDE
OF AN EQUATION PRODUCES AN Ê iµÕˆÛ>i˜ÌÊ Ê
Ê iµÕ>̈œ˜Ê !LGEBRA )F X A B THEN X A A Ê LÊ Ê >Ê
OR X Ê LÊ Ê >Ê #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
%XAMPLE 3OLVE AN EQUATION USING SUBTRACTION
3OLVE Y 3OLUTION
Y 7RITE ORIGINAL EQUATION
Y Ê ÎÊ Ê ÎÊ
Y Ê ÇÊ
5SE SUBTRACTION PROPERTY OF
EQUALITY 3UBTRACT Ê ÎÊ FROM
EACH SIDE
3IMPLIFY
4HE SOLUTION IS Ê ÇÊ #(%#+
2EMEMBER TO CHECK
YOUR SOLUTION IN THE
ORIGINAL EQUATION
FOR ACCURACY
7RITE ORIGINAL EQUATION
Y Ê ÇÊ 3UBSTITUTE Ê ÇÊ FOR Y
Ê
3OLUTION CHECKS
Ê £äÊ %XAMPLE 3OLVE AN EQUATION USING ADDITION
3OLVE T 3OLUTION
T 7RITE ORIGINAL EQUATION
T Ê ™Ê Ê ™Ê
T Ê ÓäÊ
5SE ADDITION PROPERTY OF
EQUALITY !DD Ê ™Ê TO EACH
SIDE
3IMPLIFY
4HE SOLUTION IS Ê ÓäÊ #(%#+
T Ê ÓäÊ Ê ££Ê ,ESSON s !LGEBRA .OTETAKING 'UIDE
7RITE ORIGINAL EQUATION
3UBSTITUTE Ê ÓäÊ FOR T
3OLUTION CHECKS
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
#HECKPOINT 3OLVE EACH EQUATION #HECK YOUR SOLUTION
A Ê
Ê >ÊÊ££Ê
Ê
Ê
Ê
Ê
Ê
Ê
Ê
Ê LÊÊәÊ
X Ê
B Ê ÝÊÊxÊ
Y Ê ÞÊÊÓ
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7ORDS
-ULTIPLYING EACH SIDE OF AN EQUATION BY
THE SAME NONZERO NUMBER PRODUCES AN
Ê iµÕˆÛ>i˜ÌÊiµÕ>̈œ˜Ê X
X
z B AND A s THEN A + ]z Ê >Ê + Ê LÊ
!LGEBRA )F ]
A
A
OR X Ê >LÊ $)6)3)/. 02/0%249 /& %15!,)49
7ORDS
$IVIDING EACH SIDE OF AN EQUATION BY THE SAME
NONZERO NUMBER PRODUCES AN Ê iµÕˆÛ>i˜ÌÊ Ê
Ê iµÕ>̈œ˜Ê L
L
AX
z
zOR
X
!LGEBRA )F AX B AND A s THEN ]
A
>
>
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
3OLVE AN EQUATION USING DIVISION
%XAMPLE 3OLVE X 4HE DIVISION
PROPERTY OF
EQUALITY CAN BE
USED TO SOLVE
EQUATIONS INVOLVING
MULTIPLICATION
3OLUTION
X X n
7RITE ORIGINAL EQUATION
5SE DIVISION PROPERTY OF EQUALITY
$IVIDE EACH SIDE BY Ê nÊ n
X Ê ÇÊ
3IMPLIFY
4HE SOLUTION IS Ê ÇÊ #(%#+
7RITE ORIGINAL EQUATION
X Ê ÇÊ 3UBSTITUTE Ê ÇÊ FOR X
Ê xÈÊ %XAMPLE 3OLUTION CHECKS
3OLVE AN EQUATION USING MULTIPLICATION
A
3OLVE ]z 4HE MULTIPLICATION
PROPERTY OF EQUALITY
CAN BE USED TO
SOLVE EQUATIONS
INVOLVING DIVISION
3OLUTION
A
A
Ê xÊ + ]
z Ê xÊ + ]z A Ê ÈäÊ
7RITE ORIGINAL EQUATION
5SE MULTIPLICATION PROPERTY OF EQUALITY
-ULTIPLY EACH SIDE BY Ê xÊ 3IMPLIFY
4HE SOLUTION IS Ê ÈäÊ #(%#+
A
]z Èä
g
Ê £ÓÊ ,ESSON s !LGEBRA .OTETAKING 'UIDE
7RITE ORIGINAL EQUATION
3UBSTITUTE Ê ÈäÊ FOR A
3OLUTION CHECKS
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
3OLVE AN EQUATION BY MULTIPLYING BY A RECIPROCAL
%XAMPLE 3OLVE ]zT 3OLUTION
x
4HE COEFFICIENT OF T IS ]
z 4HE RECIPROCAL OF ]
z IS Ê ]Êz Î
Ê
x
x
Ê Ê|Ê]Êz Ê + ]
zT ÊÊ Ê|Ê]
Êz Ê + Î
Î
]zT ÊÊ
Ê
T Ê £äÊ
7RITE ORIGINAL EQUATION
-ULTIPLY EACH SIDE BY THE
x
RECIPROCAL ]Êz Î
Ê
3IMPLIFY
4HE SOLUTION IS Ê £äÊ #(%#+
]zT ]Ê
z £äÊ Ê ÈÊ 7RITE ORIGINAL EQUATION
3UBSTITUTE Ê £äÊ FOR T
3OLUTION CHECKS
#HECKPOINT 3OLVE EACH EQUATION #HECK YOUR SOLUTION
Ê
]z Ê ÝÊÊ£ÎÊ
Ê
Ê
Ê
Ê LÊÊxÓÊ
X
(OMEWORK
Ê
B
X Ê ÝÊÊÈÊ
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]
zM z
Ê “ÊÊxÈ
,ESSON s !LGEBRA .OTETAKING 'UIDE