ZXTape! 0Created with Ramsoft MakeTZX#ALG6  \  N0:0:0::236099\,502:0:0:0 q$="y"x -z$="  " K12 ,10 ;1;4;"PLEASE WAIT";0;0 "" .a=07:a,0;1;z$:a (H12 ,6;4;1;" LOADING PROGRAM ";:0 -*18,5;" " .13 ,0; / 0 2 "file" <*:15,0;"Leave tape running" F"" P*15,0;"Stop and rewind tape" R"clear (y/n) ?";q$ Tq$="y""address ? ";x ZJ17,0;"Type in file name in ";1;"UPPER CASE";0 n"Filename",a$ o015,0;"Recording " p517,0;" " x a$10 "logo"16384@,2304  '10 ,5;"Load main program" )12 ,5;"SAVE""file"" LINE 2" Z&  QnAALG6Blogo @ ??80?߀????>?#|?~???|?|~?8???1???<???????<?0~|??~?~|?|~?>??#???8??????1???????~<?|??|~?|?|~?|?|~???9??>?? ?????8<0p??>?x?~file D|&{bF| in3=6090:pc2=6050:mn3=5980\:in2=890z:pcl=850R:mn2=750:snd=730:in1=650:mn1=550&:str=100d:cls=150:cll=165:nin=200:fin=400 3000 :cls 2 1000 d**** str **** n20:.3,10 xN1;21,31;8;9 ;"*":30:=""120x #21,31;8;" ": **** cls **** u=0:v=21 **** cll **** str Bf=vu-1:f,0;" ":f  **** nin **** 30:.3,30 z=0:z$="":fs=0 ,21,z;4;0;1;"N" 2 a$= a$=12 340T ka$=13 z0a=z$:.05|L,20:21,0;" ": &a$<46.ůa$>579230 "a$=47/230 ,$fs=1Ưa$=46.230 6z=31230 @a$=46.fs=1 JN4;0;21,z;a$:.05|L,20:z=z+1:380| Tz=0230 ^a$=12 z>021,z-1;1;4;0;"N":21,z;" ":.05|L,20:z$(z)=46.fs=0 h#z=z-1:z$=z$(z):230 | z$=z$+a$  230 **** fin **** 30:.3,30 z=0:z$="" ,21,z;4;0;1;"F"  3 a$= a$=12 510 ka$=13 z0a$=z$:.05|L,20:21,0;" ": a$<33!430 z=31430 N4;0;21,z;a$:.05|L,20:z=z+1:530 a$=12 z>021,z-1;0;4;1;"F":21,z;" ":.05|L,20:z=z-1:z$=z$(z):430  430  z$=z$+a$  430 &**** mn1 **** + 4 023,6;"  " :D4,7;" ";5;" ";0;" " D<5,7;"";5;" ";0;"" ND6,7;"";5;" ";0;"" X&7,8;"" b8,12 ;"" l9 ,12 ;" " v%2:10 ,12 ;" " 11 ,12 ;""  **** in1 **** 46:0,8;lh:0,20;rh j35#:0,8;" ";0,20;" ":1,8;lh;1,20;rh:30 `1,8;" ";1,20;" ":2,8;lh;2,20;rh:30 ,2,8;" ";2,20;" " 15:2;5;1;5,13 ;f$:10 :snd:10 :2;5;0;5,13 ;f$:15 a3:9 ,14;an:30:9 ,14;" ";10 ,14;an:20  **** snd **** .3,-40(:.2~L,-29:.3,-37%:.8L,-20:.25~,-34":.2~L,-30:.5,-35#:.1}L,-5  **** mn2 **** :2:3,13 ;" " i4,13 ;"";5;" ";0;" ";5;" ";0;"" M5,13 ;"";5;" ";0;" ";5;" " k6,13 ;"";5;" ";0;" ";5;" ";0;""  '7,14;" " =8,14;" ";8,26;" " =4:11 ,14;"  " F12 ,15;" ";5;" ";0;" "  >13 ,15;"";5;" ";0;"" %F14,15;"";5;" ";0;"" *(15,16;"" /16,20;"" 4 17,20;" " 9%1:18,20;" " >19,20;"" H R**** pcl **** \str f0f=vu-1:f,0;" ":f p z**** in2 **** `6:0,16;a;0,28;a:35#:0,16;" ":1,16;a;1,28;a:30:1,16;" ":2,16;a;2,28;a:30:2,16;" ":15:2;5;1;5,16;g$;5,28;h$ `10 :snd:10 :2;5;5,16;g$;5,28;h$:15 "2:8,16;lh;8,28;rh:30:8,16;" ";8,28;" ":9 ,16;lh;9 ,28;rh:30:9 ,16;" ";10 ,16;lh;10 ,28;rh:30:10 ,16;" " 15:2;5;1;13 ,21;f$:10 :snd:10 :2;5;0; 13 ,21;f$:15 i3:17,22;lh+rh:30:17,22;" ";18,22;lh+rh:20  X3,0;6;" In the earlier lessons of~Fundamental Algebra~, you wereintroduced to machines thatchanged old numbers into newnumbers using a rule...";9 ,0;" Like for instance-";11 ,10 ;5;"x+3";13 ,0;7;" This meant 'the input number xhas three added to it'.":str ]17,1;4;"So, if you put in 4 you wouldget out 7 (as 4 + 3 = 7).":cls 3,1;5;"Another machine might have therule-";6,13 ;7;"3x";8,0;6;"which means 'multiply the inputnumber x by three'." str:12 ,1;4;"So if the input number is four,then twelve (which is 3 times 4)is the number output by themachine.":cls $6;13 ,1;"In this lesson we are going tolook at a new kind of machine,into which you can put twonumbers at the same time." .Mmn1:5,13 ;2;5;"???":u=13 :v=21:cll 85:13 ,1;"This one adds together the twonumbers you put in. So if youput 3 in the left-hand side, and4 in the right-hand side, youshould get 7.";4;19,0;"Let's try it..." B8lh=3:rh=4:an=7:f$="???":str:in1 Lu=13 :v=21:cll:10 ,14;" ":7:13 ,0;" Now you type in two numbers(they should be between 1 and9), the first for the left sideand the second for the rightside." V+nin:a<1a>9 aɺa1110V `I5:18,0;"You put ";a;" in the left-hand side,":lh=a j+nin:a<1a>9 aɺa1130j tF5:19,0;"and ";a;" in the right-hand side.":rh=a ~an=lh+rh:f$="???":in1 6u=13 :v=21:cll:10 ,14;" " 74:14,0;"Try another two numbers." +nin:a<1a>9 aɺa1180 I5:17,0;"You put ";a;" in the left-hand side,":lh=a +nin:a<1a>9 aɺa1200 F5:18,0;"and ";a;" in the right-hand side.":rh=a an=lh+rh:f$="???":in1 6u=13 :v=21:cll:10 ,14;" " [6:13 ,0;" Now, how are we to describewhat this machine does?":str 16,0;" If we call the number we put inthe left side 'a', and we callthe number we put in the rightside 'b', then we can write therule for this machine as";5;"a+b." 05,13 ;2;5;"a+b":cll "5:13 ,0;" If we put the same number inboth sides;call that number 'x',then in this special case we cansay the rule is-";17,13 ;6;"x+x":18,0;" This shows clearly that we areputting the same number (x) inboth sides of the machine." +2;5;5,13 ;"x+x" u=13  :v=21:cll  =13 ,1;"Now you input a number between1 and 9." +nin:a<1a>9 aɺa1300 d4:16,0;"You put ";a;" in both sides.":rh=a:lh=a:f$="x+x":an=2*a:in1 (f4:18,1;"Notice that the output is ";a*2;","'"which is twice ";a;".":cll 2T10 ,13 ;" ":6:13 ,0;"Try another number for 'x'." <+nin:a<1a>9 aɺa1340< Fd6:16,0;"You put ";a;" in both sides.":rh=a:lh=a:f$="x+x":an=2*a:in1 P_4:18,0;"Again, notice that the output isTWICE the input number 'x'.":cll Z14,0;7;"So we can replace the rule'x+x' by the rule '2x'.";5;2;5,13 ;" 2x":cls dmn2 nZ2;5;5,16;"2x";13 ,21;"a+b";5,28;"3x" x5:1,4;"x y":42*,163:28,0:-3,-2:70F,163:-3,2:32 ,157:47/,0 ,6:7,0;"Suppose we now" "combine our" "'a+b' machine" "with 2 single" "input mach-" "ines. The left" "hand one has" "the rule '2x'," "the right hand" "one has the" "rule '3x'." u=7:v=21:pcl ,4:7,0;" What happens" "now if we put" "the same numb-" "er into both" "of the smaller"  "machines?" ,5:14,0;"Let's try it." u=7:v=21:pcl ,5:9 ,0;"Enter a number" "between 1 and" "9." +nin:a<1a>9 aɺa1535 07:9 ,0;"You put ";a;" in"  "both machines."  " " =g$="2x":h$="3x":f$="a+b":lh=a*2:rh=a*3:in2 "3,4;a;3,10 -(lh+rh);lh+rh:42*,147:20,0:-3,-2:62>,147:-3,2 ,5u=7:v=21:pcl:18,22;" " 6;6:9 ,0;"Put in another"'"value for x." @+nin:a<1a>9 aɺa1600@ J07:9 ,0;"You put ";a;" in" T"both machines."'" " h!lh=a*2:rh=a*3:in2 r4,4;a;4,10 -(lh+rh);lh+rh:42*,139:20,0:-3,-2:62>,139:-3,2 |u=7:v=21:pcl t5:7,0;"Notice that in"'"each case the"'"output number"'"is 5 times the"'"input number.":pcl 6:7,0;"As five is the"'"sum of two and"'"three,the com-"'"bined rule of"'"2x and 3x"'"would be 5x.":7:14,0;" Therefore we"'"can write-"';4;'" 2x + 3x = 5x" pcl i7,0;6;" Let us try"'"with two other"'"single input"'"machines, 4x"'"and 7x." ^pcl:3,0;" ";4,0;" ":18,22;" " Z2;5;5,16;"4x";13 ,21;"a+b";5,28;"7x" ,6:9 ,0;"Input a common" "number 'x' as" "before and see" "what happens." +nin:a<1a>9 aɺa1780 B7:14,0;"You put ";a;" in"'"both machines." =g$="4x":h$="7x":f$="a+b":lh=a*4:rh=a*7:in2 3,4;a;3,10 -(lh+rh);lh+rh:42*,147:20,0:-3,-2:62>,147:-3,2 5u=7:v=21:pcl:18,22;" " &,7:9 ,0;"Try another..." 0+nin:a<1a>9 aɺa18400 :B4:11 ,0;"You put ";a;" in"'"both machines." D!lh=a*4:rh=a*7:in2 N4,4;a;4,10 -(lh+rh);lh+rh:42*,139:20,0:-3,-2:62>,139:-3,2 Xpcl:18,22;" " b,5:7,0;"Notice that in" l"this case, the" v"combined rule" "would be 11x," "which is made" "up from 4x and" "7x, so we can"  "write-" 4:'"4x + 7x = 11x" pcl ,6:7,0;" We can use" "these ideas to" "SIMPLIFY com-" "bined rules" "like 3x+5x to" "simple rules"  "like 8x." pcl  ,7:9 ,0;" What will" *"the simplified" 4"rule be for" > "2x+7x?" H%3:14,0;"2x+7x=" Rfin \a$"9x"2180 fA7:8,27:10 ,-8:20,30 p 2200 Y.4L,-10 :18,0;2;"No,2+7=9, so 2x+7x"'"simplifies to 9x." &3;14,6;"9x":pcl \4;9 ,0;" Now for a"'"short exercise"'"of eight ques-"'"tions.":cls  dd=0  sc=0 j=18 0c=(*9 )+1:d=(*9 )+1 )3;1,0;"Question ";j 06:4,0;"Simplify the rule-" )6,12 ;4;c;"x+";d;"x" fin:j$=(c+d)+"x" \a$=j$sc=sc+1:100d,70F:10 ,-8:20,30:2340$ j.4L,-10 :8,2;2;"As ";c;" and ";d;" is ";c+d;", so ";c;"x+";d;"x=";c+d;"x" O100d,502:40(,40(:140,502:-40(,40( $cls:j `sc<52500 t=5,3;5;"You scored ";sc;" out of eight." 2600( Ī5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of eight. You need to workthrough the exercise again.":cls:2240 ؆5:5,0;"You only answered ";sc;" correctly"'"out of eight. I suggest you lookover this lesson again later on." (str 5795160( da$=47/5160( n%fs=1Ưa$=46.5160( xz=315160( a$=46.fs=1 O4;0;21,z;a$:.05|L,20:z=z+1:5300 z=05160( a$=12 z>021,z-1;1;4;0;"N":21,z;" ":.05|L,20:z$(z)=46.fs=0 $z=z-1:z$=z$(z):5160(  z$=z$+a$  5160( **** fin **** 30:.3,30 z=0:z$="" ,21,z;4;0;1;"F"  3 a$= a$=12 54306 ka$=13 z0a$=z$:.05|L,20:21,0;" ": a$<33!5350 "z=315350 ,O4;0;21,z;a$:.05|L,20:z=z+1:5450J 6a$=12 z>021,z-1;0;4;1;"F":21,z;" ":.05|L,20:z=z-1:z$=z$(z):5350 @ 5350 J z$=z$+a$ T 5350 ^**** mn1 **** h 4 r23,6;"  " |D4,7;" ";5;" ";0;" " <5,7;"";5;" ";0;"" D6,7;"";5;" ";0;"" &7,8;"" 8,12 ;"" 9 ,12 ;" " %2:10 ,12 ;" " 11 ,12 ;""  **** in1 **** 46:0,8;lh:0,20;rh j35#:0,8;" ";0,20;" ":1,8;lh;1,20;rh:30 `1,8;" ";1,20;" ":2,8;lh;2,20;rh:30 ,2,8;" ";2,20;" " 15:2;5;1;5,13 ;f$:10 :snd:10 :2;5;0;5,13 ;f$:15 a3:9 ,14;an:30:9 ,14;" ";10 ,14;an:20  &**** snd **** 0.3,-40(:.2~L,-29:.3,-37%:.8L,-20:.25~,-34":.2~L,-30:.5,-35#:.1}L,-5 : D**** mn2 **** N:2:3,13 ;" " Xi4,13 ;"";5;" ";0;" ";5;" ";0;"" bM5,13 ;"";5;" ";0;" ";5;" " lk6,13 ;"";5;" ";0;" ";5;" ";0;"" v'7,14;" " =8,14;" ";8,26;" " =4:11 ,14;"  " F12 ,15;" ";5;" ";0;" " >13 ,15;"";5;" ";0;"" F14,15;"";5;" ";0;"" (15,16;"" 16,20;""  17,20;" " %1:18,20;" " 19,20;""  **** pcl **** str 0f=vu-1:f,0;" ":f   **** in2 ****  `6:0,16;a;0,28;a:35#:0,16;" ":1,16;a;1,28;a:30:1,16;" ":2,16;a;2,28;a:30:2,16;" ":15:2;5;1;5,16;g$;5,28;h$ *`10 :snd:10 :2;5;5,16;g$;5,28;h$:15 4"2:8,16;lh;8,28;rh:30:8,16;" ";8,28;" ":9 ,16;lh;9 ,28;rh:30:9 ,16;" ";10 ,16;lh;10 ,28;rh:30:10 ,16;" " >15:2;5;1;13 ,21;f$:10 :snd:10 :2;5;0; 13 ,21;f$:15 Hi3:17,22;lh-rh:30:17,22;" ";18,22;lh-rh:20 R \**** mn3 **** fv2,18;"      " p6,18;2;"  " z12 ,18;4;"  " E18,24;5;" " 3,19;7;" ";3,25;" ";3,29;" ";8,21;" ";14,25;" "  **** pc2 **** str 4f=vu-1:f,0;" ":f  **** in3 **** 6:0,20;a;0,26;a;0,30;a:30:0,20;" ";1,20;a;1,26;a;1,30;a:30:1,20;" " 2,20;a;2,26;a;2,30;a:30:2,20;5;"";2,26;4;"";2,30;6;"":15:2;7;1;3,19;g$;3,25;h$;3,29;i$:10 tsnd:10 :2;7;0;3,19;g$;3,25;h$;3,29;i$:15 4:4,19;lh;4,25;mi;4,29;rh:30:5;4,19;"";4;4,25;"";6;4,29;"";4;5,19;lh;5,25;mi;5,29;rh +30:5,19;" ";5,25;" ";5,29;" ";6,19;lh;6,25;mi;6,29;rh:30:6,19;" ";6,25;" ";6,29;" ";7,29;rh:15:7,29;" ";8,29;rh 15:2;7;1;8,21;f$:10 :snd:10 :2;7;0;8,21;f$ 8,29;" ";9 ,29;rh:20:9 ,29;" ";2;10 ,22;lh+mi;4;10 ,29;rh:30:10 ,22;" ";10 ,29;" ";11 ,29;rh;2;11 ,22;lh+mi:30:11 ,22;" ";11 ,29;" ";12 ,29;rh;2;12 ,22;lh+mi:30:12 ,22;" ";12 ,29;" " 10 :2;7;1;14,25;k$:10 :snd:10 :2;7;14,25;k$:10 $016,25;3;lh+rh+mi:30 .[x=1718:x-1,25;" ";3;x,25;lh+rh+mi:30:x 8 B 4 L13 ,0;" In this section we are going tofirst look at double inputmachines with the rule-";5;17,13 ;"a-b":u=13 :v=21:mn1:5,13 ;5;2;"a-b":cll V6:13 ,0;" The number that goes into theright hand side of the machineis subtracted from the one thatenters the left hand side.":cll `H7:13 ,0;"Type in a number between 6 and9 for a." j+nin:a<6a>9 aɺa6250j t216,2;4;"You made a=";a:lh=a ~>18,0;"Type in a number between 1 and4 for b." +nin:a<1a>4aɺa6280 24;21,2;"You made b=";a:rh=a 7f$="a-b":an=lh-rh:in1:cll:10 ,14;" " G5:13 ,0;"Try another number between 6 and9 for a." +nin:a<6a>9 aɺa6320 216,2;4;"You made a=";a:lh=a >18,0;"Try another number between 1 and4 for b." +nin:a<1a>4aɺa6350 24;21,2;"You made b=";a:rh=a 7f$="a-b":an=lh-rh:in1:cls:10 ,14;" " mn2:5:1,4;"x y":42*,163:28,0:-3,-2:70F,163:-3,2:32 ,157:47/,0 ,6:7,0;"Just as we did" "earlier in the"  "lesson,we com-" "bine two sing-" "le input mach-" ("ines with an" 2"'a-b' machine." <5:'"Let the left" F"hand one have" P"the rule '8x'" Z"and let the" d"right one have" n"the rule '5x'." xv2;5;5,16;"8x";5,28;"5x";13 ,21;"a-b":u=7:v=21:pcl H7:9 ,0;"Enter a number"'"for x between"'"1 and 9." +nin:a<1a>9 aɺa6540 06:13 ,0;"You put ";a;" in." =g$="8x":h$="5x":f$="a-b":lh=8*a:rh=5*a:in2 3:3,4;a;3,10 -(lh-rh);lh-rh:42*,147:20,0:-3,-2:62>,147:-3,2 Zpcl:18,22;" ":7:9 ,0;"Enter another"'"number for x." +nin:a<1a>9 aɺa6590 06:13 ,0;"You put ";a;" in." !lh=8*a:rh=5*a:in2 ܞ3:4,4;a;4,10 -(lh-rh);lh-rh:42*,139:20,0:-3,-2:62>,139:-3,2 pcl:18,22;" " 5:7,0;" Notice how"'"this time the"'"output is 3"'"times the in-"'"put and 8-5 is"'"3,so this time"'"we can write"'"the simplified"'"rule to 8x-5x"'"as 3x."''';6;" So 8x-5x=3x" Tpcl:4:9 ,0;" Simplify the"'" rule:"'';7;" 9x-4x":fin a$"5x"6690" c12 ,7;7;"=5x":3:25,20:8,-7:15,30  6700, "M.4L,-10 :15,2;2;" As 9-4=5,so"'" 9x-4x=5x." ,cls 6N10 ,0;4;"Now for a short exercise of fivequestions.":cls @ dd=0 J sc=0 Tj=15 ^Ic=(*9 )+1:d=(*9 )+1:c-d<26750^ h)3;1,0;"Question ";j r/6:4,0;"Simpify the rule-" |)6,12 ;4;c;"x-";d;"x" fin:j$=(c-d)+"x" \a$=j$sc=sc+1:100d,70F:10 ,-8:20,30:6830 l.4L,-10 :8,1;2;"As ";c;" minus ";d;" is ";c-d;", so ";c;"x-";d;"x=";c-d;"x" O100d,502:40(,40(:140,502:-40(,40( cls:j sc<36870 <5,3;5;"You scored ";sc;" out of five."  6890 ֨5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":cls:6730J 5:5,0;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on." str h4;14,0;"We will now look at a morecomplicated combination ofmachines."  cls:mn3 2;7;3,19;"3x";3,25;"5x";3,29;"4x";8,22;"a+b";14,25;"a+b" /6:4,0;" The larger mach-" "ines both have" &"the rule 'a+b'." 0"The small mach-" :"ines have the" D"rules '3x', '5x'," N "and '4x'." Xpc2 b5:1,4;"x y":42*,163:28,0:-3,-2:70F,163:-3,2:32 ,157:47/,0 l&7,0;" Again we must" v"enter a common" "number for 'x'." "Type in a number" "between 1 and 9." +nin:a<1a>9 aɺa7070 07:15,0;"You made x equal"  "to ";a;"." _g$="3x":h$="5x":k$="a+b":i$="4x":lh=3*a:mi=5*a:rh=4*a:f$=" a+b":in3 Ф3:3,4;a;3,10 -(lh+rh+mi);lh+rh+mi:42*,147:12 ,0:-3,-2:546,147:-3,2 6u=7:v=21:pc2:18,25;" " 86:9 ,0;"Try another value"'"for x." +nin:a<1a>9 aɺa7150 <7;12 ,0;"You made x equal"'"to ";a;"." /lh=3*a:rh=4*a:mi=5*a:in3  3:4,4;a;4,10 -(lh+rh+mi);lh+rh+mi:42*,139:12 ,0:-3,-2:546,139:-3,2 pc2:18,25;" "  6:7,0;" Notice how in"'"this case the"'"value of x is"'"multiplied by 12"'"which is 3+5+4."'"So we can write"'"that:"'';7;" 3x+5x+4x=12x":str *717,0;5;" Simplify:"''" 2x+4x+7x" 4fin >a$"13x"7260\ H$19,10 ;5;"=13x" RN3:115s,20:8,-7:18,27:7280p \f=217-1:f,0;" ":f:.4L,-10 :9 ,0;2;" As 2+4+7=13,"'" 2x+4x+7x=13x." fV3:20,30:40(,40(:60<,30:-40(,40( phcls:4:9 ,0;" Now try this last exercise."''" There are ten questions.":cls z dd=0  sc=0 j=110 Hc=(*9 )+1:d=(*9 )+1:e=(*9 )+1 )3;1,0;"Question ";j 06:4,0;"Simplify the rule-" 16,10 ;4;c;"x+";d;"x+";e;"x=" fin:j$=(c+d+e)+"x" ʂa$=j$sc=sc+1:100d,70F:10 ,-8:20,30:7;6,19;c+d+e;"x":7400 u.4L,-10 :8,1;2;" As ";c;"+";d;"+";e;"=";c+d+e;",so ";c;"x+";d;"x+";e;"x=";c+d+e;"x." O100d,502:40(,40(:140,502:-40(,40( cls:j sc<67440 ;5,3;5;"You scored ";sc;" out of ten."  7460$ 5:dd=0dd=1:5,0;;"You only answered ";sc;" correctly"'"out of ten. You need to workthrough the exercise again.":cls:7300 5:5,0;"You only answered ";sc;" correctly"'"out of ten. I suggest you lookover this lesson again later on." $str .L6;14,0;" Now work through Exercise 6b inthe workbook." 8@17,0;"Don't forget to check all youranswers." Lcls:2700 &"":5 &+"file"9899&:"usr""a",168: ' "":"" ncn\nzcRnnnn&tdllii  uvza cdG3xH5xKa+bI4xF a+beJ9xZALLusr X??x<579230 "a$=47/230 ,$fs=1Ưa$=46.230 6z=31230 @a$=46.fs=1 JN4;0;21,z;a$:.05|L,20:z=z+1:380| Tz=0230 ^a$=12 z>021,z-1;1;4;0;"N":21,z;" ":.05|L,20:z$(z)=46.fs=0 h#z=z-1:z$=z$(z):230 | z$=z$+a$  230 **** fin **** 30:.3,30 z=0:z$="" ,21,z;4;0;1;"F"  3 a$= a$=12 510 ka$=13 z0a$=z$:.05|L,20:21,0;" ": a$<33!430 z=31430 N4;0;21,z;a$:.05|L,20:z=z+1:530 a$=12 z>021,z-1;0;4;1;"F":21,z;" ":.05|L,20:z=z-1:z$=z$(z):430  430  z$=z$+a$  430 L0:0:6: `1,0;" In this lesson we are going tolook at even more complicatedrules and how we can simplifythem."'';4;" For example we can simplify therule-" t39 ,0;5;" 3x+5x+2x+7x" ~;4:11 ,0;"by first adding the numbers-" I5:13 ,12 ;"3+5+2+7"'';4;"This comes to 17, so" 117,8;"3x+5x+2x+7x=";7;"17x" cls M5:9 ,0;"Now try a short exercise of fivequestions.":cls  dd=0  sc=0 j=15 `b=(*9 )+1:c=(*9 )+1:d=(*9 )+1:e=(*9 )+1 )3;1,0;"Question ";j 06:4,0;"Simplify the rule-" 66,8;4;b;"x+";c;"x+";d;"x+";e;"x" fin:j$=(b+c+d+e)+"x" a$=j$sc=sc+1:7;6,19;"=";a$:100d,70F:10 ,-8:20,30:1300  .4L,-10 :8,0;2;"As ";b;"+";c;"+";d;"+";e;"=";b+c+d+e;", so ";b;"x+";c;"x+";d;"x+";e;"=";b+c+d+e;"x" X2:100d,502:40(,40(:140,502:-40(,40( cls:j sc<31340< (<5,3;5;"You scored ";sc;" out of five." 2 1360P <5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":cls:1210 F5:5,0;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on." Pcls Z5:2,0;" Do you remember how in theearly lessons of ~FundamentalAlgebra~, you learned how tosolve simple equations like-" dg4;7,13 ;"3x=12";5;9 ,0;" You used the inverse rule to 3xon 12." n}6:12 ,0;" That is, you divided 12 by 3,changing the equation to-";15,13 ;4;"x=123" xP17,0;"which gave the solution-";4;19,14;"x=4" cls z6:0,0;" But suppose we were asked tosolve the equation-";7;3,10 ;"3x+5x+2x=20" 5,0;" First we must simplify theequation, and that means in thiscase we must simplify the lefthand side-" d7;10 ,12 ;"3x+5x+2x";6;12 ,0;"Which becomes ";5;"10x." 14,0;"The equation is now-";7;16,13 ;"10x=20";18,0;6;"which we can solve by dividing20 by 10 to give the solution-";21,15;7;"x=2" cls 4:3,0;"We now look at another equation-";5;5,12 ;"5x-2x=9";7,0;4;"First simplify the left handside-";9 ,14;5;"3x=9";4;11 ,0;"Then apply the inverse rule tothe right hand side-";5;14,13 ;"x=93";4;16,0;"Which gives the solution-";5;18,14;"x=3" cls H9 ,0;7;"Now try a short exercise of fivequestions." cls  dd=0  sc=0 j=15 mc=(*9 )+1:d=(*19)-9 :xx=(*9 )+1:c+d<1d=01540  !u$=c+"x":d>0u$=u$+"+"  u$=u$+d+"x="+((c+d)*xx) )3;1,0;"Question ";j 16:4,0;"Solve the equation-" "6,11 ;4;u$ ,"8,0;"Therefore, x=" 6nin @a=xxsc=sc+1:3;8,13 ;a:3:100d,70F:10 ,-8:20,30:1630^ J.4L,-10 :2:8,13 ;xx;5;" (as ";xx*(c+d);"";c+d;"=";xx;")":100d,502:40(,40(:140,502:-40(,40( ^cls:j hsc<31670 r<5,3;5;"You scored ";sc;" out of five." | 1690 5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":cls:1520 5:5,0;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on." cls 5:0,0;" Before going on to morecomplicated equations, let ushave a look at other EXPRESSIONSor rules which are a mixture of'+' and '-' rules." 47:6,0;" For example: 5x-3x+7x" 5:8,0;" We would simplify this inexactly the same way as we didwith the ones we looked atearlier on." Q13 ,0;"First work out the sum-";7;15,13 ;"5-3+7" *17,0;"Which comes to 9, so" +7;19,10 ;"5x-3x+7x=9x" cls M7;9 ,0;"Now try a short exercise of fivequestions.":cls  dd=0  sc=0 j=15 c=(*9 )+1:d=(*19)-9 :e=(*19)-9 :c+d+e<1(d>0e>0)(d=0e=0c=0)1810 !v$=c+"x":d>0v$=v$+"+" !$v$=v$+d+"x":e>0v$=v$+"+" &v$=v$+e+"x" 0)3;1,0;"Question ";j :06:4,0;"Simplify the rule-" D6,11 ;4;v$ Nfin Xa$=(c+d+e)+"x"7;6,19;"=";a$:sc=sc+1:3:100d,70F:10 ,-8:20,30:1910v b.4L,-10 :2:8,2;"As ";v$(1);v$(34);v$(67);"=";c+d+e;", so ";v$;"=";c+d+e;"x." lX2:100d,502:40(,40(:140,502:-40(,40( vcls:j sc<31950 <6:5,3;"You scored ";sc;" out of five."  1980 5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":cls:1790 5:5,0;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on." cls Ə5:1,0;" Using what we have learned sofar we can now solve equationslike-";4;5,9 ;"3x-2x+8x-3x=18" Э7,0;"The left hand side simplifiesto-";4;10 ,7;"6x";6;10 ,11 ;"(as 3-2+8-3=6)";4;12 ,12 ;"so 6x=18" ڕ14,0;"Applying the inverse rule of 6xto 18, we get-";4;17,13 ;"x=186";19,9 ;6;"Therefore x=3" cls H6:9 ,0;"Now try a short exercise of fivequestions." cls  dd=0  sc=0 j=15  c=(*9 )+1:d=(*19)-9 :e=(*19)-9 :xx=(*9 )+1:c+d+e<1(d>0e>0)(d=0e=0)2080  *!v$=c+"x":d>0v$=v$+"+" 4$v$=v$+d+"x":e>0v$=v$+"+" >v$=v$+e+"x="+((c+d+e)*xx) H)3;1,0;"Question ";j R16:4,0;"Solve the equation-" \6,11 ;4;v$ f+8,0;6;"Therefore, x=" pnin za=xxsc=sc+1:3;8,13 ;a:3:100d,70F:10 ,-8:20,30:2190 .4L,-10 :2:8,13 ;xx;5;" (as ";xx*(c+d+e);"";c+d+e;"=";xx;")":100d,502:40(,40(:140,502:-40(,40( cls:j sc<32230 <5,3;5;"You scored ";sc;" out of five."  2250 5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":cls:2060  5:5,0;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on." str ԍ6;11 ,0;" Now try Exercise Seven in theworkbook."''" Don't forget to check all youranswers, and do all corrections." cls ` 5000 6:0:0: ‡x=010 :l$:5,0+x*3;l$:.05|L,40(-(2*x):x:"F","U","N","D","A","M","E","N","T","A","L" ̱7,2;" " ,3;14,10 ;"LESSON SEVEN" str  in2=890z:pcl=850R:mn2=750:snd=730:in1=650:mn1=550&:str=100d:cls=150:cll=165:nin=200:fin=400 0:7:0:  5480h **** str **** 80P:.3,10 O1;21,31;8;9 ;"*":30:=""5060 #21,31;8;" ": **** cls **** u=0:v=21 **** cll **** str Bf=vu-1:f,0;" ":f   **** nin **** 30:.3,30 (z=0:z$="":fs=0 2,21,z;4;0;1;"N" < 2 Fa$= Pa$=12 5280 Zka$=13 z0a=z$:.05|L,20:21,0;" ": d'a$<46.ůa$>57951702 na$=47/51702 x%fs=1Ưa$=46.51702 z=3151702 a$=46.fs=1 O4;0;21,z;a$:.05|L,20:z=z+1:5310 z=051702 a$=12 z>021,z-1;1;4;0;"N":21,z;" ":.05|L,20:z$(z)=46.fs=0 $z=z-1:z$=z$(z):51702  z$=z$+a$  51702 **** fin **** 30:.3,30 z=0:z$="" ,21,z;4;0;1;"F"  3 a$= a$=12 5440@ ka$=13 z0a$=z$:.05|L,20:21,0;" ": "a$<33!5360 ,z=315360 6O4;0;21,z;a$:.05|L,20:z=z+1:5460T @a$=12 z>021,z-1;0;4;1;"F":21,z;" ":.05|L,20:z=z-1:z$=z$(z):5360 J 5360 T z$=z$+a$ ^ 5360 h5:1,0;" In this section we are going tolook at some more equations andthe methods we use to solvethem."''" First we are going to studyequations like-";4;9 ,13 ;"3x-2=4" ro11 ,0;" Notice that the rule on theleft hand side (";3;"LHS";5;" for short)" |113 ,0;"is a CHAIN of simple rules:" [6:15,2;"FIRST- input number 'x' is multiplied by three." I18,2;"THEN - two is taken away from the result." cls 4:3,0;" When we solved simple equationsearlier, we applied the inverserule of that on the LHS to thenumber on the right hand side(";6;"RHS";4;" for short), and that gaveus the solution to the equation." N11 ,0;7;" But in this equation we have achain of rules." E6:16,0;"What is the inverse rule of achain?" cls t5:3,0;" Well, we work BACKWARDS,applying the inverse rules tothe number on the RHS." :7:7,0;" First, ADD 2 to the RHS-" ^9 ,13 ;3;"4+2=6";7;11 ,0;" Then DIVIDE the RHS by 3-" %3;13 ,13 ;"63=2" I15,0;5;" Which gives the solution ";3;"x=2." cls i6:4,0;" We should just check that, byputting the value two into therule 3x-2:" /8,8;3;"3x2-2=4, or 6-2=4" I10 ,0;"Therefore both sides of theequation are equal." &;16,0;"Let's try another equation likethat." 0cls :V7:2,0;"Solve the equation-";4;4,12 ;"5x+6=21" D6,0;"The LHS rule is 'multiply x by 5and add 6'."''"So first we SUBTRACT 6 from theRHS-";3;12 ,0;" 5x=21-6, which gives 5x=15" N14,0;"Then we DIVIDE the RHS by 5-";6;16,13 ;"x=155";7;18,0;"Which gives the solution ";5;"x=3." Xcls b}4:2,0;" To summarise our method forsolving these kind of equations,here are three steps to follow." l5:7,0;"1) Study the rule on the left hand side (LHS)."''"2) Apply the inverse rules in reverse order to the number on the right hand side (RHS)." vV14,0;"3) Check your solution by putting it into the LHS rule." S18,0;6;" Before you do an exercise, hereis one more example." cls q5:2,0;"Solve the equation-";3;4,12 ;"2x-5=17";5;6,0; 6,0;"The LHS rule is 'multiply x by 2and subtract 5'."''"So first we ADD five to the RHS-";3;11 ,0;" 2x=17+5, which gives 2x=22" 13 ,0;"Then we DIVIDE the RHS by 2-";3;15,13 ;"x=222";5;17,0;"Which gives the solution ";7;"x=11." Rcls:4;9 ,0;"Now for a short exercise of fivequestions.":cls  dd=0  sc=0 j=15 Jc=(*9 )+1:e=(*19)-9 :xx=(*9 )+1 &c*xx+e<1e=05850 !v$=c+"x":e>0v$=v$+"+" v$=v$+e+"="+((c*xx)+e) )3;1,0;"Question ";j  16:4,0;"Solve the equation-" 6,11 ;4;v$  +8,0;6;"Therefore, x=" *nin 4a=xxsc=sc+1:3;8,13 ;a:3:100d,70F:10 ,-8:20,30:5960H >.4L,-10 :2:8,13 ;xx:100d,502:40(,40(:140,502:-40(,40( Hcls:j Rsc<36000p \<5,3;5;"You scored ";sc;" out of five." f 6020 p5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":cls:5830 z5:5,0;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on." cls 7:1,0;" Now suppose we had an equationlike-";3;4,11 ;"3x+2x-4=6";7;6,0;" First we simplify the LHS usingwhat we have learned in previoussections.";6;10 ,6;"3x+2x-4 becomes 5x-4" 12 ,0;"So the equation is now-";5;14,13 ;"5x-4=6";7;16,0;"This can be solved by-" 4:18,0;" a) 5x=6+4 b) 5x=10 c) x=105 d) x=2" cls 6:1,0;" Here is another example. Thistime the equation is-";5;4,9 ;"7x-3x+2x+6=18";6;6,0;" First we simplify the LHS usingwhat we have learned in previoussections.";3;10 ,4;"7x-3x+2x+6 becomes 6x+6" 12 ,0;"So the equation is now-";3;14,12 ;"6x+6=18";6;16,0;"This can be solved by-" ʉ7:18,0;" a) 6x=18-6 b) 6x=12 c) x=126 d) x=2" Rcls:4;9 ,0;"Now for a short exercise of fivequestions.":cls  dd=0  sc=0 j=15 c=(*9 )+1:xx=(*9 )+1:b=(*19)-9 :d=(*19)-9 :e=(*19)-9 :xx*(c+b+d)+e<1(b=0d=0e=0)c+b+d<16140 !v$=c+"x":d>0v$=v$+"+" $v$=v$+d+"x":b>0v$=v$+"+" $v$=v$+b+"x":e>0v$=v$+"+" $v$=v$+e+"="+(xx*(c+d+b)+e) .)3;1,0;"Question ";j 816:4,0;"Solve the equation-" B6,11 ;4;v$ L+8,0;6;"Therefore, x=" Vnin `a=xxsc=sc+1:3;8,13 ;a:3:100d,70F:10 ,-8:20,30:6290 j.4L,-10 :2:8,13 ;xx:100d,502:40(,40(:140,502:-40(,40( t5;17,0;"Solution:":7:17,13 ;c+d+b;"x";v$(9 10 );"=";xx*(c+d+b)+e:18,13 ;c+d+b;"x=";xx*(c+b+d)+e;:e>0"-";:6280 ~"+"; xe:19,13 ;c+d+b;"x=";xx*(c+d+b):20,13 ;"x=";xx*(c+d+b);"";c+d+b:21,13 ;"x=";xx cls:j sc<36330 <5,3;5;"You scored ";sc;" out of five."  6350 5:dd=0dd=1:5,0;"You only answered ";sc;" correctly"'"out of five. You need to workthrough the exercise again.":cls:6120 Ć5:5,0;"You only answered ";sc;" correctly"'"out of five. I suggest you lookover this lesson again later on." cls t1,0;" Now try exercise seven in theworkbook. Be sure to check allanswers and do all corrections." dcls x40,10 ;5;1;"LESSON SEVEN" :5,1;6;"That completes Lesson Seven." 6;7,1;"If you would like to go over"'" Lesson Seven again, ";10 ,13 ;2;6;"PRESS R":'" otherwise:-";12 ,13 ;6;1;"PRESS S" =""6550 ="R"Ŧ="r"5 ="S"Ŧ="s"6600   6550  ܓ5,0;5;" When you are ready to begin thePost Test, type NEW followedby-";7;1;9 ,10 ;"LOAD ~ALGP~" 23636T\,255: &"ALG7"5: '"" anzcRnnnn&tdllii  uvce zbdV 2x-3x+2x+9=15Z55A LL!  ALGP vB in2=890z:pcl=850R:mn2=750:snd=730:in1=650:mn1=550&:str=100d:cls=150:cll=165:nin=200:fin=400 0:7:0: ay(7):f=17:y(f):f:1,2,2,3,3,4,4 ( 3000 2 1000 d**** str **** n20:.3,10 xN1;21,31;8;9 ;"*":30:=""120x #21,31;8;" ": **** cls **** u=0:v=21 **** cll **** str Bf=vu-1:f,0;" ":f  **** nin **** 30:.3,30 z=0:z$="":fs=0 ,21,z;4;0;1;"N" 2 4a$=:a$=13 fs=1z=1250 a$=12 340T ka$=13 z0a=z$:.05|L,20:21,0;" ": &a$<46.ůa$>579230 "a$=47/230 ,$fs=1Ưa$=46.230 6z=31230 @a$=46.fs=1 JN4;0;21,z;a$:.05|L,20:z=z+1:380| Tz=0230 ^a$=12 z>021,z-1;1;4;0;"N":21,z;" ":.05|L,20:z$(z)=46.fs=0 h#z=z-1:z$=z$(z):230 | z$=z$+a$  230 **** fin **** 30:.3,30 z=0:z$="" ,21,z;4;0;1;"F"  3 a$= a$=12 510 ka$=13 z0a$=z$:.05|L,20:21,0;" ": a$<33!430 z=31430 N4;0;21,z;a$:.05|L,20:z=z+1:530 a$=12 z>021,z-1;0;4;1;"F":21,z;" ":.05|L,20:z=z-1:z$=z$(z):430  430  z$=z$+a$  430 L6:2,0;" This Post Test contains sevenquestions matched to the sevenminimum objectives set out inthe instruction booklet." V5:8,0;" After you type in your answerit is checked and at the end ofthe test you will be given amark out of seven, a list of thequestions you got wrong and theobjectives not achieved." `e4:15,0;" Based on this you will be givenrecommendations for your futurestudy." jcls t7:5,0;" Because this test uses arandomising routine, each run ofthe Post Test will produce adifferent set of questions, soit can be used to advantage inyour revision programme." ~cls  dd=0  sc=0  q(7) 0c=(*9 )+1:d=(*9 )+1 (3;1,0;"Question 1" 06:4,0;"Simplify the rule-" )6,13 ;4;c;"x+";d;"x" fin .7;8,5;"Your answer: ";a$ 2a$=(c+d)+"x"q(1)=1:sc=sc+1 cls Ic=(*9 )+1:d=(*9 )+1:c-d<11260 (3;1,0;"Question 2" 06:4,0;"Simplify the rule-"  )6,13 ;4;c;"x-";d;"x" fin .7;8,5;"Your answer: ";a$ (2a$=(c-d)+"x"q(2)=1:sc=sc+1 2cls