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Examples: 3x + 4x = 7x 13xy 9xy = 4xy 12x3y2 - 5x3y2 = 7x3y2 Can you simplify? 4x3 + 4y3 11x2 7x 6x3y + 5xy3 Simplify the following: 1) 7x + 5 3x2) 6w2 + 11w + 8w2 15w3) 6x + 4 + 15 7x4) (12x 5) (7x 11)5) (2x2 - 3x + 7) (-3x2 + 4x 7)6) 11a2b 12ab2 WORKING WITH THE DISTRIBUTIVE PROPERTY Example: 3(2x 5) + 5(3x +6) = Since in the order of operations, multiplication comes before addition and subtraction, we must get rid of the multiplication before you can combine like terms. We do this by using the distributive property: 3(2x 5) + 5(3x +6) = 3(2x) 3(5) + 5(3x) + 5(6) = 6x - 15 + 15x + 30 = Now you can combine the like terms: Final answer: 6x + 15x = 21x 3(2x 5) + 5(3x + 6) = 21x + 15 -15 + 30 = 15 Practice Examples: 1) 4(7x - 8) + 6(5x + 10) 2) 6(4x2 5x + 2) + 3(-8x2 + 11x + 4) 3) 5(4x2 8x + 3) 7(6x2 4x + 11)4) 4(6x3 4x2 + 7x + 1) 9(4x3 2x2 - 6x + 1)5) 10(4x2 + 8x + 7) 8(5x2 + 10x 9)6) 6(4x2 3x +2) + 5(3x 6)7) 9(4x2 7x + 12) 12(3x2 5x 9)8) 4(6x3 4x2 + 11) 7(5x2 + 9) 9) 3(12x4 16x3 + 4x2 8x + 24) 4(9x4 12x3 3x2 6x + 18)Solving Equations Golden Rule of Algebra: Do unto one side of the equal sign as you will do to the other **Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other side. If you multiply by -2 on the left side, you have to multiply by -2 on the other. If you subtract 15 from one side, you must subtract 15 from the other. You can do whatever you want (to get the x by itself) as long as you do it on both sides of the equal sign. Solving Single Step Equations: To solve single step equations, you do the opposite of whatever the operation is. The opposite of addition is subtraction and the opposite of multiplication is division. Solve the following equations for x: 1) x + 5 = 122) x 11 = 193) 22 x = 174) 5x = -305)  QUOTE   = 36)  QUOTE   x = - 87) x + 15 = 288) 15 x = 219)  QUOTE   = 510) 6 + x = 3411) 9x = 4512) 7 + x = 19 Solving Multi-Step Equations: 3x 5 = 22 To get the x by itself, you will need to get rid of the 5 and the 3. +5 +5 Get rid of addition and subtraction first. ***Use the opposite order of PEMDAS*** 3x= 27 Then, we get rid of multiplication and division. 33 x = 9 We check the answer by putting it back in the original equation: Check: 3x 5 = 22 We have that x = 9 3(9) - 5 = 22 27 - 5 = 22 22 = 22 (It checks!) Solve the Multi-Step Equations and check: 1) 9x - 11 = -38Check:2) 160 = 7x + 6Check:3) 32 - 6x = 53 Check:4) x - 11 = 16Check:5) 4x 7 = -23 Check:6) 12x + 9 = - 15 Check:7) 21 4x = 45 Check:8)  QUOTE   - 4 = 4 Check:9)  QUOTE   +3 = 7 Check:10) 26 = 60 2x Check:Equations with more than one x on the same side of the equal sign: You need to simplify (combine like terms) and then use the same steps as a multi-step equation. 9x + 11 5x + 10 = -15 9x 5x = 4x 11 + 10 = 21 1st combine like terms 4x + 21 = -15 Now it looks like a multistep equation that we already did -21 -21 Use subtraction to get rid of the addition. 4x = -36 Now divide to get rid of the multiplication 4 4 x = -9 We check the answer by putting it back in the original equation: Check: 9x + 11 5x + 10 = -15 We have that x = -9 9(-9) + 11 5(-9) + 10 = -15 -81 + 11 + 45 + 10 = -15 -70 + 55 = -15 -15 = -15 (It checks!) Solve the Multi-Step Equations and check: 1) 15x - 24 - 4x = -79 Check:2) 102 = 69 - 7x + 3x Check:3) 3(2x - 5) - 4x = 33 Check:4) 3(4x - 5) + 2(11 - 2x) = 43Check:5) 9(3x + 6) - 6(7x - 3) = 12 Check:6) 7(4x - 5) - 4(6x + 5) = -91Check:Equations with x's on BOTH sides of the equal sign: You need to "Get the x's on one side and the numbers on the other." Then you can solve. Example: 12x 11 = 7x + 9 -7x -7x Move the xs to one side. 5x 11 = 9 Now it looks like a multistep equation that we did in the 1st section. +11 +11 Add to get rid of the subtraction. 5x = 20 Now divide to get rid of the multiplication 5 5 x = 4 We check the answer by putting it back in the original equation: Check: 12x 11 = 7x + 9 We have that x = 4 12(4) 11 = 7(4) + 9 48 11 = 28 + 9 37 = 37 (It checks!) Solve the Multi-Step Equations and check: 1) 11x - 3 = 7x + 25 Check:2) 22 - 4x = 12x + 126 Check:3) x - 12 = x -6 Check:4) 5(2x + 4) = 4(3x + 7) Check:5) 12(3x + 4) = 6(7x + 2) Check:6) 3x- 25 = 11x - 5 + 2x Check: Homework 9-25-2008 Solving Multi-Step Equations (multiple variables = same side) 1-  QUOTE   2-  QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE   3-  QUOTE   4-  QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE   5-  QUOTE   6-  QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE   Answers: PAGE 6: 1-  QUOTE   2-  QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE     QUOTE    QUOTE   3-  QUOTE   4-  QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE     QUOTE    QUOTE    QUOTE     QUOTE   5-  QUOTE   6-  QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE    QUOTE     QUOTE    QUOTE        PAGE 1  ! 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Y¨SF>tTJPHʱ1Py2 ݴ2ba,b q}Ȯoйr/)Sq3QFueV("AyTGc]\mz•(K#-D6#jUm*yvS,+ $FbW"Y)džQb[!b/Ը1q?Ɩ ʎWLzAd+M|UurIENDB` Dd   j 3 A5"J D 12-126 -126ib/G,Wjv7^&n/G,Wjv7PNG  IHDRtsRGB pHYs+nIDATXGX10 E_OR;K;( B( 4jn͍!٦G6jW9"nu~&v[smji 7yR?:; Y¨SF>tTJPHʱ1Py2 ݴ2ba,b q}Ȯoйr/)Sq3QFueV("AyTGc]\mz•(K#-D6#jUm*yvS,+ $FbW"Y)džQb[!b/Ը1q?Ɩ ʎWLzAd+M|UurIENDB` Dd   k 3 A6"P J 124x=28jbu腓v}yj&nu腓v}yPNG  IHDR4{9sRGB pHYs+]IDATHKu0 fKF07s8vXL@'@,ǖ\/M5tc[$KaUs\7:"s}.M?טs߄7gAx Wu?=v e~ˌ ) ,<Nʈ'YSe} kn잪\UYyܞOJK\pEZ?}8Yl0? ɖ%MsёJD 124x=28kbu腓v}yv&nu腓v}yPNG  IHDR4{9sRGB pHYs+]IDATHKu0 fKF07s8vXL@'@,ǖ\/M5tc[$KaUs\7:"s}.M?טs߄7gAx Wu?=v e~ˌ ) ,<Nʈ'YSe} kn잪\UYyܞOJK\pEZ?}8Yl0? ɖ%MsёJD 12-104=16xlbs24wsOY&nG24wsPNG  IHDROfVsRGB pHYs+IDATXGW10 {y?ѥ8.r!TlA 6|"QRz*'*Am @HSdmrh==FjD $VZ=LP?X'&#< ԕjѬ5 #,\V/jXO^2! 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Rp@"Calibri&.&1&/&Of1&x.&/&d1&Of1&x.& wix.&1& |xi&CX%7.{ @Calibr+ 4&Xx1&.&j:i.&.&yi/&|dv% % %  TUU@Č@^LName ___________________________________________________ Date ______________ Color ___________;,J...-..-..-..-..-.-...-..-..-..-..-.-..--...-..-..-..9,.-..--...-..-..011 -..-..--..-TT#UU@Č@LP 6 TUU@Č@j L`Algebra I5+.0 ,TTUU@Č@jLP k TT'UU@Č@jLP ,TT(SUU@Č@(jLP @,TTTUU@Č@TjLP ,TTUU@Č@jLP ,TT UU@Č@jLP u,TT  UU@Č@ jLP ,TT / UU@Č@ jLP ,TT0 [ UU@Č@0 jLP ,TT\ UU@Č@\ jLP ,TTUU@Č@jLP ,TxDUU@Č@jL\ TEUU@Č@Ej L`Miss HahlO$$9,0TTUU@Č@jLP 6Rp@Times New Roman&.& 1&/&Of1&x.& /&d1&Of1&x.& wix.&1& xiXG*Ax Times ew Romanx1&.&j:i.&.&yi/&dv% % %  Rp@Times New Roman&/& 2&|0&Of2&/& d1&2&Of2&/& wi/&2& !xiXG*Ax Times ew Roman(0&j:id0&d0&yi0&!dv% % % % % % T$7 UU@Č@9$LSimplifying and Combining Like TermsA]: !'3!A;;@;N:\: A!@;G ;4G4,],'% Ld9 9y !??% ( TT  UU@Č@ LP ;Rp@"Calibri&.&1&/&Of1&x.&/&d1&Of1&x.& wix.&1& #xi&CX%7.{ @Calibr_]H1&%i.&3&.&j:i.&.&yi/&#dv% % %  TTxUU@Č@`LP ,TT xUU@Č@`LP a,TT  xUU@Č@ `LP ,T| h xUU@Č@ `L\Exponent-(010.0TTi  xUU@Č@i `LP 6Rp@"Calibri&<-&0& .&Of0&-&/&0&Of0&-& wi-&0& &xi&CX%7.{ @Calibr@荷j1&-&j:i.&.&yi0.& &dv% % % Rp@"Calibri&p)&,&T*&Of,&)&<+&,&Of,&)& wi)&,& ,(xi&CX%7.{ @Calibr3Z$,& 3Ri*&j:i<*&<*&yid*&,(dv% % % % % % Rp@"Calibri&p)&,&T*&Of,&)&<+&,&Of,&)& wi)&,& L*xi&CX%7.{ @CalibrPf 4RPf*&j:i<*&<*&yid*&L*dv% % %  % % % TfUU@Č@ LdCoefficient 11.'.0TTgUU@Č@gLP TTA UU@Č@LP ,% % % TXB y UU@Č@B LP4x?6% % % TT k UU@Č@ LP2)% % % TT m UU@Č@ LP % % % TTn  UU@Č@n LP ,% % % T -UU@Č@ LpVariable (or Base)4, ,0.0 2,#.TT.cUU@Č@.LP 6 % % % TXUU@Č@nL&" WMFC P* 2% % % T jUU@Č@n LWrite the coefficients, variableR .0.&1.'.0$*+ ,0.TkE UU@Č@knLts, and exponents of$,00-(010.0$1TTC W UU@Č@C nLP TX A UU@Č@X n Lhthe following0.11B0+TTB Y UU@Č@B nLP:TTZ  UU@Č@Z nLP 6Rp @Times New Roman&.& 1&/&Of1&x.& /&d1&Of1&x.& wix.&1& l,xiXG*Ax Times ew Romanx1&.&j:i.&.&yi/&l,dv% % %  TTK  UU@Č@K LP 6 TTK  lUU@Č@K WLP 6 TTK n UU@Č@K LP 6 TTK  RUU@Č@K =LP 6 TTK T UU@Č@K LP 6 TTK  8UU@Č@K #LP 6 TTK : UU@Č@K LP 6 TTK  UU@Č@K LP a6 TTK  UU@Č@K |LP 6 Rp @Times New Roman&/& 2&|0&Of2&/& d1&2&Of2&/& wi/&2& |-xiXG*Ax Times ew Roman(0&j:id0&d0&yi0&|-dv% % % % % % T UU@Č@ L`Like TermsC8,C,,R'' % Ld  !??% ( % % % T` UU@Č@LT: a% % % TD  UU@Č@)LTerms that have identical variable parts -. J$0,0,*.0.0',*, ,0.0, $TT   UU@Č@ LP(T   UU@Č@ Lxsame variable(s) and s$+J.*, ,0.$,00$T  UU@Č@ Llame exponent(s))+J..(/10.0#T` UU@Č@LT. TT UU@Č@LP 6 TT w UU@Č@_ LP 6Rp  @"Calibri1&/&Of1&x.&/&d1&Of1&x.& wix.&1& #xi&CX7.{ @Calibr_]&%i.&3&.&j:i.&.&yi/&#dvdv% Rp @"Calibriuwuwr)KCXCuw:I&EE{ @HxL -&v؃EBxL؀ETEXE,&<&owswCuwuw-uw! x'EXEXfvx'EHxLh.&.&'vcvdv% ( Rp  @"Calibriuwuwr)KxL -&v؃EBxLCuw:I&EE~ HyLv؃E| ~ &uw~ Z ,-&:fvE:fv"&Z ~ `v-uw!,&Z <&ZcvU5fv:fv!v~ xV9!xV'vcvdv% ( % (  Tw  UU@Č@ !LWhen simplifying using addition aR0.0$J0*0+0$0+,/010,Tw  UU@Č@ Llnd subtraction, 00$00 ,&10Tdw w UU@Č@ LTyou )10Tx w 5 UU@Č@x ;Lcombine  like terms by keeping the "like term" and adding '0J00.')..J#'/*)..00+0.%*..J%,00,000+ % % % T ?W UU@Č@? Lpor subtracting the1 $00 ,&0+0.% % % TT@ XV UU@Č@@? LP % % % TY W UU@Č@Y? L|numerical coefficients.o0/J. &,'0.'.0$TT W UU@Č@? LP o6 TTW  UU@Č@ LP 6 Rp @ Calibri&/&2&|0&Of2&/&d1&2&Of2&/& wi/&2& .xi&CX%7.{ @Calibrj "i @(0&j:id0&d0&yi0&.dv% % % % % % T| 7 UU@Č@ L\Examples-(,J0.$' % Ld) . ) a!??% ( TT 7 UU@Č@ LP:TT R7 UU@Č@ LP 6% % %  % % % TT7  UU@Č@ L&" WMFC P ee,T`7  UU@Č@ LT eeT7  UU@Č@ Ld3x + 4x = 7x.(-/'./'TT7 ' UU@Č@ LP eeiTT(7 S UU@Č@( LP ee,TTT7  UU@Č@T LP ee,Tl7 C UU@Č@ LX13xy ee//'*TTD7 r UU@Č@D LP ee-TTq7  UU@Č@q LP eeT7 UU@Č@ L`9xy = 4xyee.(*./()TT 7  UU@Č@ LP ee(TT 7 / UU@Č@ LP ee,TT0 7 [ UU@Č@0 LP ee,T`\ 7 UU@Č@\ LT12xee//(% % % TT . t UU@Č@ e LP3ee% % % TT 7 ( UU@Č@ LPyee*% % % TX). Rt UU@Č@)e LP2  % % % TTS7 n UU@Č@S LP-eeTTo7  UU@Č@o LP eeTX7  UU@Č@ LP5x.(% % % TT. t UU@Č@e LP3ee% % % TT7  UU@Č@ LPy*% % % TT!. =t UU@Č@!e LP28% % % TT>7 R UU@Č@> LP TdS7  UU@Č@S LT= 7x..(% % % TT. t UU@Č@e LP3% % % TT 7 2 UU@Č@  LPy*% % % TT3. Ot UU@Č@3e LP2% % % TTP7  UU@Č@P LP 6 TT  UU@Č@ LP TT  UU@Č@ LP 6 TT  UU@Č@o LPC1T 0 UU@Č@o Llan you simplify?,0*1/$J0**TT1 f UU@Č@1o LP 6 % % % TT  UU@Č@ LP ,T`  UU@Č@ LT TX d UU@Č@ LP4x.(% % % TTe}  UU@Č@e LP3% % % TT  UU@Č@ LP Td 1 UU@Č@ LT+ 4y./*% % % TT2} N UU@Č@2 LP3% % % TTO ' UU@Č@O LP TT( S UU@Č@( LP ,TTT  UU@Č@T LP ,T`  UU@Č@ LT11x//(% % % TT} " UU@Č@ LP2% % % TT# 7 UU@Č@# LP TT8 f UU@Č@8 LP -TTe y UU@Č@e LP T`z  UU@Č@z LT7x .(TT UU@Č@ LP TT  UU@Č@ LP ,TT / UU@Č@ LP ,TT0 [ UU@Č@0 LP ,TX\ UU@Č@\ LP6x/(% % % TT } UU@Č@ LP3% % % Tx  UU@Č@ L\y + 5xy*-/'*% % % TT}  UU@Č@ LP3% % % TT  UU@Č@ LP TT  UU@Č@ LP 6 TT f UU@Č@N LP 6 % % % T|f  UU@Č@ L\Simplify*J0*TTf  UU@Č@ LP Tf  UU@Č@ Lhthe following/.10B0+' % Ld   '!??% ( TTf  UU@Č@ LP:TTf  UU@Č@ LP 6!y  TX JUU@Č@2Ly P1)/TT JUU@Č@2Ly P Tx xJUU@Č@2Ly \7x + 5 /(-.TTy JUU@Č@y2Ly P .TT JUU@Č@2Ly P TX JUU@Č@2Ly P3x/'TT >JUU@Č@2Ly P .!y " " !#  % % %  TXN JUU@Č@N2L# P2)/TT NJUU@Č@2L# P TXO JUU@Č@O2L# P6w/B% % % TX &" WMFC UU@Č@L# P2  % % % T JUU@Č@2 L# `+ 11w + 8w../A./B% % % TX UU@Č@ L# P2  % % % TT JUU@Č@ 2L# P .TT JUU@Č@ 2L# P T` JUU@Č@ 2L# T15w/.ATT JUU@Č@ 2L# P .!# " " ! s % % %  TX A JUU@Č@ 2L sP3)/TTB JUU@Č@B 2L sP @T &JUU@Č@2 L sd6x + 4 + 15 /(-../.TT' UJUU@Č@'2L sP .TTU hJUU@Č@U2L sP TXi JUU@Č@i2L sP7x/'TT JUU@Č@2L sP .! s" " ' % Ldu x u !??%  % Ldu x u !??% ( ' % Ldy  y !??% ( ' % Ld "  !??% ( ' % Ld# # !??% ( ' % Ld !??% ( ' % Ld r !??% ( ' % Lds v s !??%  % Lds v s !??% ( ' % Ldu xu  !??% ( ' % Ld "  !??% ( ' % Ld   !??% ( ' % Lds vs  !??% ( !y % % %  TXWUU@Č@?LyP4)/TTWUU@Č@?LyP TlWUU@Č@?LyX(12x /.(TTWUU@Č@?LyP .TTWUU@Č@?LyP T`5WUU@Č@?LyT5) /TT6dWUU@Č@6?LyP .TTdxWUU@Č@d?LyP TdyWUU@Č@y?LyT(7x /(TT-WUU@Č@?LyP .TT-@WUU@Č@-?LyP T`AWUU@Č@A?LyT11)//TTWUU@Č@?LyP .!y" " !#  % % %  TXNWUU@Č@N?L# P5)/TTWUU@Č@?L# P ST`]WUU@Č@?L# T(2x/(% % % TX^$UU@Č@^L# P2  % % % TTWUU@Č@?L# P-TTWUU@Č@?L# P T| WUU@Č@?L# \3x + 7) /'./TT  WUU@Č@ ?L# P .TT  WUU@Č@ ?L# P TT # WUU@Č@ ?L# P(TT$ > WUU@Č@$ ?L# P-TX?  WUU@Č@? ?L# P3x/(% % % TT  $UU@Č@ L# P2% % % TT  WUU@Č@ ?L# P Tl t WUU@Č@ ?L# X+ 4x ./(TTu  WUU@Č@u ?L# P .TT  WUU@Č@ ?L# P TX  WUU@Č@ ?L# P7).TT / WUU@Č@ ?L# P .!# " " ! s % % %  TX A WUU@Č@ ?L sP6)/TTB WUU@Č@B ?L sP \T`'WUU@Č@?L sT11a//,% % % TT(D$UU@Č@(L sP2% % % TXEWUU@Č@E?L sPb 0TTWUU@Č@?L sP .TTWUU@Č@?L sP TdWUU@Č@?L sT12ab//,&" WMFC t0% % % TT$UU@Č@L sP2% % % TTWUU@Č@?L sP .! s" " ' % Lduxu!??% ( ' % Ldyy!??% ( ' % Ld"!??% ( ' % Ld# #!??% ( ' % Ld   !??% ( ' % Ld r !??% ( ' % Ldsvs!??% ( ' % Lduxu!??% ( ' % Lduxu!??%  % Lduxu!??% ( ' % Ldyy!??% ( ' % Ld"!??% ( ' % Ld"!??% ( ' % Ld# #!??% ( ' % Ld   !??% ( ' % Ld   !??% ( ' % Ld r !??% ( ' % Ldsvs!??% ( ' % Ldsvs!??%  % Ldsvs!??% (  % % %  TTUU@Č@LP ,TTUU@Č@LP -Rp {@"Calibri&.&1&/&Of1&x.&/&d1&Of1&x.& wix.&1& /xi&CX%7.{ @Calibrx1&.i 4&Xx1&.&j:i.&.&yi/&/dv% % %  T0UU@Č@}&LWORKING WITH THE DISTRIBUTIVE PROPERTYyZKI#XUy#BTCTAT#?BL#KWB#OAGKZGAKBFTTCUU@Č@}LP O % % % TTUU@Č@LP 6 % % % T|UU@Č@hL\Example:-(,J0.' % LdrwrV!??% ( TxUU@Č@hL\ Tl?UU@Č@hLX3(2x /.(TT@nUU@Č@@hLP .TTnUU@Č@nhLP TUU@Č@hLl5) + 5(3x +6) = /./.(..-TTUU@Č@hLP 6 TUU@Č@ L`Since in *0'.0TUU@Č@fLthe order of operations, multiplication comes before addition and subtraction, we must get rid of the 0.1 0.11/. +10$J00',10&0J.#0.1.,0010,00$00 +'10B-J0#+. 01/.Rp @"Calibri&.&1&/&Of1&x.&/&d1&Of1&x.& wix.&1& 0xi&CX%7.{ @Calibrukj3&x1&.&j:i.&.&yi/&0dv% % %  % % % T`UU@Č@HLlmultiplication J00',10Rp@ Calibri&/&2&|0&Of2&/&d1&2&Of2&/& wi/&2& 1xi&CX%7.{ @Calibrj "i(0&j:id0&d0&yi0&1dv% % % % % % Tp`UU@Č@HLXbefo&" WMFC Tre1.1!.'% LdPWP!??% ( % % % TT`UU@Č@HLP T `UU@Č@H5Lyou can combine like terms. We do this by using the )10&,0'0J00.)..J$R-010#0*0$0+/.% % % T `UU@Č@ HLxdistributive property1% 11 ,.1!11.!+% % % TT`UU@Č@HLP:TT`UU@Č@HLP 6 Tl(`UU@Č@(LX3(2x /.(TT` UU@Č@LP .TT `UU@Č@ LP T `/UU@Č@ Ll5) + 5(3x +6) =/./.(-/-TT0`UU@Č@0LP |TT`UU@Č@LP 6 Tp(@UU@Č@((LX3(2x) /.(TT(@UU@Č@(LP -TT';@UU@Č@'(LP T<O @UU@Č@<(L|3(5) + 5(3x) + 5(6) = //./.(-//.TdP  @UU@Č@P (LT TT  @UU@Č@ (LP 6TT  @UU@Č@ (LP 6 T`(?UU@Č@(LT6x /(TT?UU@Č@LP-TT?UU@Č@LP T?UU@Č@Lp15 + 15x + 30 =/../.(.//-TT?QUU@Č@LP 6Rp@"Calibri&<-&0& .&Of0&-&/&0&Of0&-& wi-&0& 4xi&CX%7.{ @Calibr[f@pi-&j:i.&.&yi0.&4dv% % %  % % % T  UU@Č@#LNow you can combine the like terms:;1B*10',0&0J00.0-*.. I$TT UU@Č@ LP sTTUU@Č@LP ,TT UU@Č@LP ,TT  UU@Č@ LP ,TT / UU@Č@ LP ,Rp@ Calibri&/&2&|0&Of2&/&d1&2&Of2&/& wi/&2& 7xi&CX%7.{ @CalibrB(0&j:id0&d0&yi0& 7dv% % % % % % T0 UU@Č@0  LdFinal answer*////$B,'% Ld0 0 !??% ( % % % TTUU@Č@LP:TlUU@Č@LX TTUU@Č@LP 6 T(5UU@Č@(wLh6x + 15x = 21x/(-./(.//'TT6UU@Č@6wLP JTTUU@Č@wLP ,TT UU@Č@wLP ,T  UU@Č@ w Lh TT  UU@Č@ wLP Tl  UU@Č@ wLX3(2x ./'TT  UU@Č@ wLP .TT  UU@Č@ wLP T ,UU@Č@ wLp5) + 5(3x + 6) = /...(./.T|-dUU@Č@-wL\21x + 15./'./.TTeUU@Č@ewLP 6 TT(CUU@Č@(LP-TDUU@Č@D Ld15 + 30 = 15//../...TT >UU@Č@ LP 6!PK y!R% % %  TTPhPUU@Č@P9LRP TTiPUU@Č@i9LRP 2" !RRp@Times New Roman&"& %&#&Of%&x"& #&d%&Of%&x"& wix"&%& ,9xiXG*Ax Times ew Romanx%&"&j:i"&"&yi#&,9dv% % %   TIYPUU@Č@I7 LRdCoefficientsH60%%006)TTZPUU@Č@Z7LRP 6" !R % % %  TePUU@Č@7 LR`VariablesN0$060+T&" WMFC 4TfPUU@Č@f7LRP 6" ! R % % %  T PUU@Č@7 L R`ExponentsB666606+TT  PUU@Č@ 7L RP 6" '% Ld!??%  % Ld!??%  % Ld{!??%  % Ld!??%  % Ldg!??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld T!??%  % Ld   !??%  % Ld   !??%  % LdQ!??%  % LdQ!??%  % LdQ!??%  % LdQ!??%  % Ld  Q !??% !VRp@Times New Roman&& &p&Of && X& &Of && wi& & L;xiXG*Ax Times ew RomanxV&j:iX&X&yi&L;dv% % % % % %  % % %  TXyUU@Č@LVP8c2,% % % TTzoUU@Č@zLVP2"% % % TTUU@Č@LVP 2" !V % % %  TTE]UU@Č@ELVP TT^UU@Č@^LVP 2" !V % % %  TTUU@Č@LVP TTUU@Č@LVP 2" !V  % % %  TTUU@Č@LV P TT UU@Č@LV P 2" % LdRUR!??%  % LdRUR{!??%  % LdRUR!??%  % LdRURg!??%  % LdRUR!??%  % LdRUR!??%  % LdRUR!??%  % LdR URT!??%  % Ld R U R!??%  % LdVV!??%  % LdVV!??%  % LdVV!??%  % LdVV!??%  % Ld V  V!??% ! % % %  TX*HUU@Č@*LP9x22TTHUU@Č@LP 2" ! % % %  TTEp]UU@Č@ELP TT^pUU@Č@^LP 2" ! % % %  TTpUU@Č@LP TTpUU@Č@LP 2" !  % % %  TTpUU@Č@L P TTp UU@Č@L P 2" % Ld!??%  % Ld{!??% &" WMFC   % Ld!??%  % Ldg!??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld T!??%  % Ld   !??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld   !??% ! % % %  TT3bUU@Č@3jLPy0% % % TTcKUU@Č@c<LP8#% % % TTUU@Č@jLP 2" ! % % %  TTE9]UU@Č@ELP TT^9UU@Č@^LP 2" ! % % %  TT9UU@Č@LP TT9UU@Č@LP 2" !  % % %  TT9UU@Č@L P TT9 UU@Č@L P 2" % Ld!??%  % Ld{!??%  % Ld!??%  % Ldg!??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld T!??%  % Ld   !??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld   !??% !u % % %  T`jJUU@Č@3LuT12a22,% % % TTjUU@Č@jLuP2"% % % TTJUU@Č@3LuPb2% % % TTUU@Č@LuP3!% % % TTJUU@Č@3LuP 2" !u % % %  TTE]sUU@Č@E\LuP TT^sUU@Č@^\LuP 2" !u % % %  TTsUU@Č@\LuP TTsUU@Č@\LuP 2" ! u % % %  TTsUU@Č@\L uP TT sUU@Č@\L uP 2" % Ld!??%  % Ld{!??%  % Ld!??%  % Ldg!??%  % Ld!??%  % Ld!??%  % Ld!??%  % Ld T!??%  % Ld   !??%b &WMFC   % Ldt!??%  % Lduxu!??%  % Lduxu!??%  % Lduxu{!??%  % Ldt!??%  % Lduxu!??%  % Lduxug!??%  % Ldt!??%  % Lduxu!??%  % Lduxu!??%  % Ldt!??%  % Lduxu!??%  % Ldu xuT!??%  % Ld  t !??%  % Ld u x u!??%  % Ld u x u!??% " F(GDICy6 !b $$>>_888% '%  [L~/  ;]H0 H;;]GlI]G+G % % $$AA( " FGDICF(GDIC = !b $$>>_888% %  [L ;  WKOO(oWWKPNNOP % % $$AA( " FGDICF(GDIC  !b $$>>_888% %  [L   -\OOX,\+-\OQNNOOQ % % $$AA( " FGDIC% % ( 666666666666666666666666666666666666 6 66 6  6 66 6  6 66 6  6 66 6  6 66 6 66666666666666666666  c.@Times New Roman---  2 2c 2 c1 2  c ,c'@"Calibri---2 =2^cName ___________________________________________________ Date ______________ Color ___________ 2 =&c 2 J2 cAlgebra I 2 JZc 2 Jzc $ 2 Jc $ 2 Jc $ 2 Jc $ 2 J c $ 2 J.c $ 2 JRc $ 2 Jvc $ 2 Jc $ 2 Jc #2 Jc 52 J cMiss Hahl  2 Jc @Times New Roman---@Times New Roman------A2 Z$cSimplifying and Combining Like Terms      - @ !\- 2 Zc @"Calibri--- 2 hc $ 2 h c $ 2 h.c $2 hRcExponent 2 h|c @"Calibri---@"Calibri------@"Calibri------2 y cCoefficient  2 yc  2 yc $---2 yc4x--- 2 r*c2--- 2 t/c --- 2 t@c $---&2 ydcVariable (or Base) 2 yc ---2 2c* ---;2 ; cWrite the coefficients, variable (2 cs, and exponents of 2 c 2  cthe following 2 Yc: 2 \c @Times New Roman- - -  2 <c  2 <c  2 <c  2 <c  2 <c  2 <c  2 <c  2 <c  2 <c @Times New Roman- - - - - - 2 2 cLike Terms - @ !<2- ---2 nc: o---I2 w)cTerms that have identical variable parts   2 *c(,2 .csame variable(s) and s #2 came exponent(s)) 2 c. o 2 c  2 2c  @"Calibri- @"Calibri-   @"Calibri-  - =2 .2!cWhen simplifying using addition ar  #2 .cnd subtraction, 2 .cyou d2 .";ccombine like terms by keeping the "like term" and adding    ---&2 ;2cor subtracting the--- 2 ;c ---.2 ;cnumerical coefficients.  2 ;c  2 I2c @ Calibri- - - ---2 V2cExamples - @ !+W2- 2 V]c: 2 V_c ------ 2 d2c $2 dVc m2 d^ c3x + 4x = 7x 2 dc 2 dc $ 2 dc $2 dc13xy l 2 dc 2 dc 2 d c9xy = 4xy 2 d.c $ 2 dRc $ 2 dvc $2 dc12xy--- 2 _c3--- 2 dcy---2 _c2 --- 2 dc- 2 dc 2 dc5x--- 2 _c3--- 2 dcy--- 2 _c2--- 2 dc 2 dc= 7x--- 2 _c3--- 2 dcy--- 2 _c2--- 2 dc  2 q2c  2 q5c  2 ~2cC#2 ~8can you simplify? 2 ~c --- 2 2c $2 Vc x2 ^c4x--- 2 hc3--- 2 lc 2 nc+ 4y--- 2 c3--- 2 c  2 c $ 2 c $2 c11xy--- 2 c2--- 2 c  2 c 2 c 2 c7x y 2 c  2 .c $ 2 Rc $ 2 vc $2 c6x--- 2 c3---2 cy + 5xys--- 2 c3--- 2 c  2 c  2 2c ---2 2cSimplify  2 Vc 2 X cthe following- @ !a2- 2 c: 2 c ,-2 2-1) 2 ;- 12 l-7x + 5 y 2 - 2 - 2 -3x 2 - ,-'',--- 2 2) 2  2 6w---2  2 ---2  + 11w + 8w---2 D2 --- 2 I 2 O 2 Q15w+ 2 d ,'',6--- 2 63) 2 6 '2  66x + 4 + 15  2 6 2 6 2 67x 2 6 ,6''- @ !--- @ !-- - @ !-- - @ !- - @ !- - @ !- - @ !- - @ !6-- @ !6- - @ !?-- - @ !?- - @ !?- - @ !?6- ,:---- 2 2-:4) 2 ;-: 2 X-:(12x 5 2 n-: 2 s-: 2 v-:5) x 2 -: 2 -: 2 -:(7x  2 -: 2 -: 2 -:11)  2 -: ,:-'',:--- 2 :5) 2 : 2 :(2x ---2 :2 --- 2 :- 2  : 2  :3x + 7)  2 ,: 2 1:  2 4:( 2 7:-2 ::3x--- 2 E:2--- 2 H: 2 K:+ 4x 7 2 _: 2 e: 2 g:7) 2 p: ,:'',:6--- 2 6:6) 2 6: *2 6:11ax--- 2 6:2---2 6:b  2 6: 2 6: 2 6:12ab--- 2 6:2--- 2 6: ,:6''- @ !-- - @ !-- - @ !- - @ !- - @ !- - @ !- - @ !6- - @ !Q-- - @ !:--- @ !:-- - @ !:-- - @ !Q- - @ !:- - @ !:- - @ !Q- - @ !:- - @ !:- - @ !Q6- - @ !:6-- @ !:6- ---  2 E2c $ 2 EVc @"Calibri- - - D2 X&cWORKING WITH THE DISTRIBUTIVE PROPERTY           2 Xc --- 2 f2c ---2 t2cExample: - @ !)u2- 2 t[c :2 tmc3(2x  2 tc 2 tc #2 tc5) + 5(3x +6) =  2 tc 2 2 cSince in 2 Wfcthe order of operations, multiplication comes before addition and subtraction, we must get rid of the   @"Calibri- - - ---"2 2cmultiplication @ Calibri---- - - 2 scbefore- @ !s---- 2 c [2 5cyou can combine like terms. We do this by using the   - - - +2 cdistributive property--- 2 c: 2 c 2 c3(2x e 2 c 2 c "2 c5) + 5(3x +6) = 2 c  2  c 2 c3(2x)  2 c 2 c /2 c3(5) + 5(3x) + 5(6) = 2 c  2 'c  2 .c 2 c6x  2 c- 2 c %2 c15 + 15x + 30 =6 2 c @"Calibri------@2 2#cNow you can combine the like terms:   2 c  2 c $ 2  c $ 2 .c $ 2 Rc $@ Calibri------2 v cFinal answer- @ !8v---- 2 c:2 c  2 c  2 c6x + 15x = 21x 2 c 2 c $ 2  c $2 . c  2 Nc 2 Qc3(2x  2 fc 2 lc %2 nc5) + 5(3x + 6) = 62 c21x + 15 2 c  2 c-2  c15 + 30 = 15 2 c ,<(,_2--- 2 G2_  2 J2_ ',_@Times New Roman--- 2 e _Coefficients 2 _ ',--- 2 Variables  2  ',2--- 2 2Exponents 2 *2 '- @ !1-- @ !1-- @ !-2-- @ !_-- @ !I`-- @ !-- @ !@-- @ !-- @ !G-- @ !2-- @ !2-- @ !1-- @ !_-- @ !-- @ !-- @ !2-,_2@Times New Roman--------- 2 A2_8c--- 2 L2_2--- 2 P2_ ',_---  2 _  2 _ ',---  2   2  ',2---  2 2  2 2 '- @ !1-- @ !-2-- @ !_-- @ !I`-- @ !-- @ !@-- @ !-- @ !G-- @ !2-- @ !1-- @ !_-- @ !-- @ !-- @ !2-,_2--- 2 B2_9x 2 N2_ ',_---  2 _  2 _ ',---  2   2  ',2---  2 2  2 2 '- @ !1-- @ !-2-- @ !_-- @ !I`-- @ !-- @ !@-- @ !-- @ !G-- @ !2-- @ !1-- @ !_-- @ !-- @ !-- @ !2-,_2---  2 C2_y--- 2 I2_8--- 2 M2_ ',_---  2 _  2 _ ',---  2   2  ',2---  2 2  2 2 '- @ !1-- @ !-2-- @ !_-- @ !I`-- @ !-- @ !@-- @ !-- @ !G-- @ !2-- @ !1-- @ !_-- @ !-- @ !-- @ !2-,_2--- 2 92_12a --- 2 J2_2--- 2 N2_b--- 2 T2_3--- 2 X2_ ',_---  2 _  2 _ ',---  2   2  ',2---  2  2  2 2 '- @ !1-- @ !-2-- @ !_-- @ !I`-- @ !-- @ !@-- @ !-- @ !G-- @ !2-- @ !1-- @ !1-- @ !1-- @ !-2-- @ !_-- @ !_-- @ !I`-- @ !-- @ !-- @ !@-- @ !-- @ !-- @ !G-- @ !2-- @ !2-- @ !2-'--8utvvuruxr--'--8Oe1n1lOdOe3p,n1j3p--'--8av1v1uatav2x,v2r2x--'"System???????????--ccccccbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaa՜.+,0 hp   BoobadomeO{+ %Simplifying and Combining Like Terms Title  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`acdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry FIData b1Table.WordDocument4SummaryInformation(,xDocumentSummaryInformation8CompObjy  F'Microsoft Office Word 97-2003 Document MSWordDocWord.Document.89q