3OLVE 4WO3TEP %QUATIONS
'OAL + 3OLVE TWOSTEP EQUATIONS
9OUR .OTES
)$%.4)&9).' /0%2!4)/.3
)DENTIFY THE OPERATIONS INVOLVED IN THE EQUATION
X /PERATIONS PERFORMED ON X
-ULTIPLY BY
!DD
Ê ÎÊ Ê ÇÊ 3UBTRACT
Ê ÇÊ $IVIDE BY
Ê ÎÊ 3OLVE A TWOSTEP EQUATION
%XAMPLE 7HEN SOLVING A
TWOSTEP EQUATION
APPLY THE INVERSE
OPERATIONS IN THE
REVERSE ORDER OF THE
ORDER OF OPERATIONS
/PERATIONS TO ISOLATE X
3OLVE X 3OLUTION
X 7RITE ORIGINAL EQUATION
X Ê ÇÊ Ê ÇÊ
X Ê £ÓÊ
X
Î
Î
X Ê {Ê
3UBTRACT Ê ÇÊ FROM EACH
SIDE
3IMPLIFY
$IVIDE EACH SIDE BY Ê ÎÊ 3IMPLIFY
4HE SOLUTION IS Ê {Ê #(%#+
X 7RITE ORIGINAL EQUATION
Ê {Ê 3UBSTITUTE Ê {Ê FOR X
Ê Ê £ÓÊ -ULTIPLY BY Ê {Ê Ê
3IMPLIFY 3OLUTION CHECKS
,ESSON s !LGEBRA .OTETAKING 'UIDE
Ê £™Ê #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY
9OUR .OTES
#HECKPOINT 3OLVE THE TWOSTEP EQUATION #HECK YOUR
SOLUTION
R
]z z
Ê
Ê ÀÊÊÓnÊ
%XAMPLE K Ê ŽÊÊn
3OLVE A TWOSTEP EQUATION BY COMBINING LIKE TERMS
3OLVE A A 3OLUTION
A A Ê Ç>Ê Ç>
z Ç
Ç
A Ê ™Ê
7RITE ORIGINAL EQUATION
#OMBINE LIKE TERMS
$IVIDE EACH SIDE BY Ê ÇÊ 3IMPLIFY
4HE SOLUTION IS Ê ™Ê #(%#+
A A Ê ™Ê Ê ™Ê Ê ÎÈÊ zÊ ÓÇÊ 7RITE ORIGINAL EQUATION
3UBSTITUTE Ê ™Ê FOR A
-ULTIPLY BY Ê ™Ê AND BY Ê ™Ê Ê ÈÎÊ !DD 3OLUTION CHECKS
#HECKPOINT 3OLVE THE EQUATION #HECK YOUR SOLUTION
Z Z Ê
Ê âÊÊ{Ê
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B B Ê LÊÊÎ
,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
&IND AN INPUT OF A FUNCTION
%XAMPLE 4HE OUTPUT OF A FUNCTION IS MORE THAN TIMES THE
INPUT &IND THE INPUT WHEN THE OUTPUT IS 3OLUTION
3TEP 7RITE AN EQUATION FOR THE FUNCTION ,ET X BE THE
INPUT AND Y BE THE OUTPUT
Y Ê {ÝÊÊÓÊ ÊÊÊÊÊÊ Y IS MORE THAN TIMES X
3TEP 3OLVE THE EQUATION WHEN Y Ê
Ê
Y Ê {ÝÊÊÓÊ
7RITE ORIGINAL FUNCTION
Ê £{ÊÊÊÊÊÊÊ Ê {ÝÊÊÓÊ
3UBSTITUTE Ê £{Ê FOR Y
Ê £{ÊÊÓÊ Ê {ÝÊÊÓÊzÓÊ
Ê £ÓÊ zÊ {ÝÊ
£Ó
{
{Ý
3UBTRACT Ê ÓÊ FROM EACH
SIDE
3IMPLIFY
$IVIDE EACH SIDE BY Ê {Ê {
Ê ÎÊ zX
3IMPLIFY
!N INPUT OF Ê ÎÊ PRODUCES AN OUTPUT OF Ê £{Ê #(%#+
Y Ê {ÝÊÊÓÊ
7RITE ORIGINAL FUNCTION
Ê £{Ê Ê {­Î®ÊÊÓÊ
3UBSTITUTE Ê £{Ê FOR Y
AND Ê ÎÊ FOR X
Ê £{Ê Ê £ÓÊÊÓÊ
-ULTIPLY Ê {Ê AND Ê ÎÊ Ê £{Ê zÊ £{Ê
3IMPLIFY 3OLUTION CHECKS
#HECKPOINT 3OLVE THE EQUATION #HECK YOUR SOLUTION
4HE OUTPUT OF A FUNCTION IS LESS THAN TIMES THE
INPUT &IND THE INPUT WHEN THE OUTPUT IS (OMEWORK
Ê
Ê ÝÊÊÎ
,ESSON s !LGEBRA .OTETAKING 'UIDE
#OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY