f04qY6odEY		

N-(+o7H'!;BBEFORE WE GET STARTED, THERE ARE A FEW NUMBER FACTS WE SHOULD
6KNOW.  ANSWER EACH QUESTION AND CHECK YOUR ANSWER
$BEFORE PUSHING THE "RETURN" KEY.
12+31=?
43
,THAT'S GOOD!  LET'S TRY ANOTHER PROBLEM.
(NO, THE ANSWER SHOULD HAVE BEEN 43.
47+25=?
72
6YOU SEEM TO UNDERSTAND ADDITION OF WHOLE NUMBERS.
"SO GO ON TO THE NEXT SEGMENT.
*SORRY, THE ANSWER SHOULD HAVE BEEN 72.
53+78=?
131
,VERY NICE! CONTINUE TO THE NEXT SEGMENT.
<SORRY, THE ANSWER SHOULD HAVE BEEN 131.  PLEASE SEE YOUR
TEACHER FOR WORKSHEET 1.
82+17=?
99
*HURRAH!  CONTINUE TO THE NEXT SEGMENT.
6OOPS!  THE ANSWER SHOULD HAVE BEEN 99.  PLEASE SEE
"YOUR TEACHER FOR WORKSHEET 1.
-10+27=?
17
&GOOD WORK. LET'S TRY ANOTHER ONE.
4NO, IT SHOULD HAVE BEEN 17.  LET'S TRY ANOTHER.
PROBLEM.
-23+18=?
-5
(GREAT, MOVE ON TO THE NEXT SEGMENT.

:NO, THE ANSWER SHOULD HAVE BEEN -5.  LET'S TRY ANOTHER
PROBLEM.
	-35+72=?
37
,THAT'S RIGHT.  MOVE TO THE NEXT SEGMENT.
	>NO, THE ANSWER SHOULD HAVE BEEN 37.  YOU SEEM TO NEED MORE
:HELP BEFORE WE CONTINUE.  PLEASE SEE YOUR TEACHER FOR
WORKSHEET 2.
-25+12=?
-13
(NICE JOB!  MOVE TO THE NEXT SEGMENT.

@NO, THE ANSWER SHOULD HAVE BEEN -13.  YOU SEEM TO NEED MORE
FHELP BEFORE WE CONTINUE.  PLEASE SEE YOUR TEACHER FOR WORKSHEET 2.
14+-20=?
-6
GOOD!  TRY ANOTHER ONE.
2NO, IT SHOULD HAVE BEEN -6.  TRY ANOTHER ONE.
35+-12=?
23
*FANTASTIC!  MOVE TO THE NEXT SEGMENT.
2NO, IT SHOULD HAVE BEEN 23.  TRY ANOTHER ONE.
42+-59=?
-17
THAT'S IT!  TRY ANOTHER.
>NO, IT SHOULD HAVE BEEN -17.  YOU SEEM TO NEED MORE HELP. 
,PLEASE SEE YOUR TEACHER FOR WORKSHEET 3.
57+-38=?
19
&GREAT!  MOVE TO THE NEXT SEGMENT.
<NO, IT SHOULD HAVE BEEN 19.  YOU SEEM TO NEED MORE HELP.
,PLEASE SEE YOUR TEACHER FOR WORKSHEET 3.
-15+-23=?
-38
*EXCELLENT!  CONTINUE TO THE NEXT ONE.
:SORRY, THE ANSWER IS -38.  REMEMBER WHEN YOU ADD TWO 
6NEGATIVE NUMBERS YOUR ANSWER IS A NEGATIVE NUMBER.
-42+-57=?
-99
DTERRIFIC!  YOU ARE NOW READY TO FIND MISSING VARIABLES IN SIMPLE
EQUATIONS.  GOOD LUCK!
BSORRY, THE ANSWER IS -99.  REMEMBER, WHEN YOU ADD TWO NEGATIVE
.NUMBERS YOUR ANSWER IS A NEGATIVE NUMBER.
-67+-28=?
-95
GOOD JOB.
HSORRY, THE ANSWER IS -19.  PLEASE SEE YOUR TEACHER FOR WORKSHEET 4.
-25+-87=?
-112
4RIGHT!  CONTINUE TOTHE NEXT SEGMENT. GOOD LUCK.
<SORRY THE ANSWER IS -112.  PLEASE SEE YOUR TEACHER  FOR
WORKSHEET 4.
4NOW LET'S TRY SOME PROBLEMS INVOLVING VARIABLES.
:REMEMBER THAT A VARIABLE IS A LETTER USED TO REPRESENT
*A  NUMBER IN A MATHEMATICAL SENTENCE.
:FOR EXAMPLE THE SENTENCE X+15 REPRESENTS 27 WHEN X=12.
  NOW YOU TRY SOME.
0FIND THE VALUE OF THE SENTENCE X+34 IF X=-22
12
$GOOD JOB!  TRY ANOTHER PROBLEM.
:NO, THE ANSWER SHOULD HAVE BEEN 12 BECAUSE -22+34=12.
TRY ANOTHER ONE.
$FIND THE VALUE OF 53+X IS X=-39.
14
.GREAT!  YOU ARE READY TO SOLVE EQUATIONS.
:NO, THE ANSWER SHOULD HAVE BEEN 14 BECAUSE 53+-39=14.
TRY ANOTHER ONE.
$FIND THE VALUE OF 82+X IF X=-57.
25
&THAT'S THE IDEA.  TRY ANOTHER ONE.
DNO, THE ANSWER SHOULD HAVE BEEN 25 BECAUSE 82+-57=25.  YOU SEEM
:TO NEED MORE HELP BEFORE WE CONTINUE.  PLEASE SEE YOUR
TEACHER FOR WORKSHEET 5.
&FIND THE VALUE OF X+-52 IF X=-17.
-69
2THAT'S GOOD. YOU ARE READY TO SOLVE EQUATIONS.
BNO, THE ANSWER SHOULD HAVE BEEN -69 BECAUSE -17+-52=-69.  YOU
FSEEM TO NEED MORE HELP.  PLEASE SEE YOUR TEACHER FOR WORKSHEET 5.
@NOW, LET'S LEARN TO SOLVE EQUATIONS.  WE WILL START WITH THE
DEQUATION X+15=26.  SOLVING EQUATIONS MEANS THAT WE HAVE TO FIND
DA NUMBER TO REPLACE X TO MAKE THE STATEMENT TRUE.  IN THIS CASE
<WHEN WE SOLVE FOR X WE FIND THAT WHEN X=11, THE EQUATION
IS A TRUE STATEMENT.
L     YOU WILL NOW HAVE EQUATIONS TO SOLVE. IF YOU GET ALL OF THE ANSWERS
HCORRECT, THEN YOU MAY MOVE ON TO MORE DIFFICULT EQUATIONS.  HOWEVER,
HIF YOU MISS SOME, WE WILL GO OVER THE PROCESS OF SOLVING EQUATIONS.
         GOOD LUCK!
*SOLVE FOR X.  TYPE IN JUST THE ANSWER.
X+53=85
X=
32
GOOD START!
FNO, THE CORRECT ANSWER IS 35.  LET'S GO OVER THE STEPS INVOLVED IN
SOLVING EQUATIONS.
SOLVE FOR X.
-35+X=12
X=
47
THAT'S RIGHT AGAIN!
HNO, THE CORRECT ANSWER IS 47.  LET'S GO OVER THE STEPS INVOLVED IN 
SOLVING EQUATIONS.
SOLVE FOR X.
X+22=-47
X=
-69
ANOTHER ONE RIGHT! GREAT.
HNO, THE CORRECT ANSWER IS -69.  LET'S GO OVER THE STEPS INVOLVED IN
SOLVING EQUATIONS.
SOLVE FOR X.
-65+X=-79
X=
-14
SUPER!  YOU GOT IT RIGHT.
HNO, THE CORRECT ANSWER IS -14.  LET'S GO OVER THE STEPS INVOLVED IN
SOLVING EQUATIONS.
SOLVE FOR X.
X+-23=-11
X=
12
JFANTASTIC!  IF YOU GET THE NEXT ONE RIGHT, WE WILL TRY MORE DIFFICULT
EQUATIONS.
DNO, THE CORRECT ANSWER IS 12.  LET'S GO OVER THE STEPS INVOLVED
IN SOLVING EQUATIONS.
SOLVE FOR X.
42+X=19
X=
-23
EXCELLENT WORK!
BYOU OBVIOUSLY UNDERSTAND HOW TO SOLVE THESE EQUATIONS.  PLEASE
BSEE YOUR TEACHER FOR SOME WORK WITH MORE DIFFICULT EQUATIONS.
PNO, THE CORRECT ANSWER IS -23.  LET'S GO OVER THE STEPS INVOLVED IN SOLVING
EQUATIONS.
(WHAT IS THE ADDITIVE INVERSE OF 15?
-15
THAT'S RIGHT.
DNO, THE ANSWER SHOULD HAVE BEEN -15.  LET'S REVIEW WHAT THE TERM
ADDITIVE INVERSE MEANS.
 (WHAT IS THE ADDITIVE INVERSE OF -38?
38
(GOOD, NOW LET'S WORK WITH EQUATIONS.
"JNO, THE ANSWER SHOULD HAVE BEEN 38.  LET'S REVIEW WHAT IS MEANT BY THE
TERM ADDITIVE INVERSE.
 <THE ADDITIVE INVERSE OF A NUMBER X IS THAT NUMBER WHICH
YOU ADD TO X TO GET ZERO.
<  FOR EXAMPLE, THE ADDITIVE INVERSE OF 25 IS -25 BECAUSE
25+-25=0.
:  THE ADDITIVE INVERSE OF -82 IS 82 BECAUSE -82+82=0.
>  NOTICE, THE ADDITIVE INVERSE OF A NUMBER IS POSITIVE IF
@THE NUMBER IS NEGATIVE, AND THE ADDITIVE INVERSE OF A NUMBER
*IS NEGATIVE IF THE NUMBER IS POSITIVE.
:  ALSO, A NUMBER AND ITS ADDITIVE INVERSE ALWAYS HAVE
6THE SAME ABSOLUTE VALUE; THAT IS A NUMBER AND ITS
8ADDITIVE INVERSE ARE THE SAME DISTANCE FROM 0 ON THE
NUMBER LINE.
,NOW, WHAT IS THE ADDITIVE INVERSE OF 27?
-27
$THAT'S RIGHT.  TRY ANOTHER ONE.
LNO, THE ANSWER SHOULD HAVE BEEN -27.  PLEASE SEE YOUR TEACHER FOR EXTRA 
&EXTRA HELP WITH ADDITIVE INVERSES.
(WHAT IS THE ADDITIVE INVERSE OF -55?
55
 THAT'S GREAT.  LET'S GO ON.
8NO, THE ANSWER SHOULD HAVE BEEN 55.  PLEASE SEE YOUR
2TEACHER FOR EXTRA HELP WITH ADDITIVE INVERSES.
8     BEFORE WE CONTINUE LET US SEE WHAT IS MEANT BY 
SOLVING AN EQUATION.
<     AN EQUATION SHOWS EQUALITY BETWEEN TWO QUANTITIES.
<     FOR EXAMPLE, X+10=25 IS AN EQUATION WHICH SAYS THAT
$SOME NUMBER X PLUS 10 EQUALS 25.
@     THIS EQUATION ALSO ASKS THE QUESTION "WHAT NUMBER PLUS
10 EQUALS 25?"
"                             
8     WHICH ONE OF THE FOLLOWING IS NOT AN EQUATION?
(             (TYPE EITHER A,B,OR C)
6 A.  X+5=12       B.  51+X=32            C.  47+X
C
GOOD WORK!
@NO, THE ANSWER IS C BECAUSE THE STATEMENT 47+X DOES NOT SHOW
EQUALITY.
#BTHE EQUAL SIGN (=) IN AN EQUATION SEPARATES THE STATEMENT INTO
TWO PARTS.
B   EVERYTHING TO THE LEFT OF THE EQUAL SIGN IS CALLED THE LEFT
:MEMBER OF THE EQUATION AND EVERYTHING TO THE RIGHT IS
,CALLED THE RIGHT MEMBER OF THE EQUATION.
B  FOR EXAMPLE, IN THE EQUATION 51+X=27 THE LEFT MEMBER IS 51+X
 AND THE RIGHT MEMBER IS 27.
   
:  IN THE FOLLOWING EQUATION WHAT IS THE RIGHT MEMBER?
       X+32=55
55

GREAT!
>NO, THE ANSWER SHOULD BE 55 BECAUSE IT IS TO THE RIGHT OF
&THE EQUAL SIGN.  TRY ANOTHER ONE.
$8IN THE FOLLOWING EQUATION WHICH IS THE LEFT MEMBER?
        10=X+5
10
2GREAT!  NOW LET'S WORK WITH SOLVING EQUATIONS.
@NO, THE ANSWER SHOULD BE 10 BECAUSE THAT IS WHAT IS TO THE 
LEFT OF THE EQUAL SIGN.
%H     TO SOLVE AN EQUATION, SUCH AS X+5=12, WE MUST FIND A NUMBER TO 
FPUT IN PLACE OF THE VARIABLE X SO THAT THE STATEMENT IS TRUE.  IN
<THIS CASE WHEN X=7 THE EQUATION IS TRUE BECAUSE 7+5=12.
H     WHEN WE SOLVE EQUATIONS WE WILL WANT TO MAKE CHANGES TO EITHER
8THE LEFT MEMBER OR THE RIGHT MEMBER OF THE EQUATION.
F     HOWEVER, BECAUSE AN EQUATION IS IN BALANCE, THAT IS, THE LEFT
FMEMBER EQUALS THE RIGHT MEMBER, IF WE MAKE A CHANGE ON ONE SIDE OF
FAN EQUATION THEN WE MUST MAKE THE SAME CHANGE ON THE OTHER SIDE OF
THE EQUATION.
(     LET'S LOOK AT A SIMPLE EXAMPLE.
         SOLVE:  X+3=10
H     TO SOLVE THIS WE MUST CHANGE THE LEFT SIDE SO IT HAS ONLY AN X.
<     LET'S USE THE IDEA OF ADDITIVE INVERSE TO HELP US.
,     WHAT IS THE ADDITIVE INVERSE OF 3?
-3

GOOD!
2NO, REMEMBER--THE ADDITIVE INVERSE OF 3 IS -3.
&F     THE NEXT STEP IN SOLVING THE EQUATION X+3=10 IS TO ADD -3 TO
DBOTH SIDES OF THE EQUATION.  (REMEMBER IF WE ADD ANYTHING TO ONE
@SIDE OF THE EQUATION WE MUST ALSO ADD IT TO THE OTHER SIDE.)
*          STARTING WITH    X + 3 = 10
*          AND ADDING -3       -3   -3
*                          ___________
(          WE GET               X = 7
    
"     LET'S DO ANOTHER EXAMPLE.
     SOLVE X+25=38.
J     FIRST WE WILL ADD THE ADDITIVE INVERSE OF 25 TO BOTH SIDES OF THE
2EQUATION.  WHAT IS THE ADDITIVE INVERSE OF 25?
-25

RIGHT!
BNO, THINK NOW, YOU KNOW THAT THE ADITIVE INVERSE OF 25 IS -25.
'@     O.K.  NOW LET'S ADD -25 TO BOTH SIDES OF THE EQUATION.
   
,         WE START WITH       X + 25 = 38
,         WE ADD -25             -25  -25
.                             ------------
>THE NEXT STEP IS TO PERFORM THE ADDITION AND SIMPLIFY THE
EQUATION.  WHAT IS 25+-25?
0

GOOD!
 NO, THINK AGAIN.  25+-25=0.
(4  WORKING WITH THE RIGHT MEMBER OF THE EQUATION;
  WHAT IS 38+-25?
13

GOOD!
NO, 38+-25=13
)0THEREFORE STARTING WITH          X + 25 = 38
0IF WE ADD                           -25  -25
0                               -------------
0WE GET                                X = 13
$AND WE HAVE SOLVED THE EQUATION.
@     TO BE SURE THAT OUR ANSWER IS CORRECT WE SHOULD PUT 13
*IN PLACE OF X IN THE EQUATION X+25=38.
D     WE THEN GET 13+25=38.  IF THIS IS A TRUE STATEMENT THEN WE
HAVE THE RIGHT ANSWER.
&     IS 13+25=38 A TRUE STATEMENT?
TYPE EITHER YES OR NO.
YES

GOOD!
0THE ANSWER SHOULD BE YES, BECAUSE 13+25=38.
**NOW, LET'S GO THROUGH ANOTHER EXAMPLE.
     -39+X=46
6FIRST WE NEED TO KNOW THE ADDITIVE INVERSE OF -39.
WHAT IS IT?
39

GOOD!
2NO, THE ADDITIVE INVERSE OF -39 IS 39 BECAUSE
-39+39=0
+6     NOW WE ADD 39 TO BOTH SIDES OF THE EQUATION.
                -39 + X = 46
                 39       39
"             ----------------

     
2  FIRST, WE WORK WITH THE LEFT MEMBER AND ADD.
   WHAT IS -39+39?
0
GOOD WORK!
NO, -39+39=0
,<     NOW, WORKING WITH THE RIGHT MEMBER, WHAT IS 46+39?
85
THAT'S RIGHT.
NO, THINK AGAIN--46+39=85
-.  THEREFORE STARTING WITH    -39 + X = 46
.  AND ADDING                  39       39
0                            ---------------
.  WE GET                           X = 85
$AND WE HAVE SOLVED THE EQUATION.
<  TO CHECK OUR ANSWER REPLACE X WITH 85 IN THE ORIGINAL
EQUATION.
  WE GET -39+85=46.
:  IS THIS A TRUE STATEMENT?  (TYPE EITHER YES OR NO.)
YES
0GOOD, WE KNOW THAT WE HAVE THE RIGHT ANSWER.
0THE ANSWER SHOULD BE YES BECAUSE -38+83=46.
>THEREFORE WE HAVE SOLVED THE EQUATION CORRECTLY AND X=85.
.(   LET'S DO ONE MORE.  SOLVE FOR X.
   X+27=15
  
2  FIRST, WE NEED TO KNOW THE ADDITIVE INVERSE
OF 27.  WHAT IS IT?
-27

RIGHT!
*NO, THE ADDITIVE INVERSE OF 27 IS -27.
/4NOW LET'S ADD -27 TO BOTH SIDES OF THE EQUATION.
$  START WITH        X + 27 = 15
$  ADD                  -27  -27
$                   -------------
 ON THE LEFT WE GET       X =
  
.WHAT VALUE DO WE GET FOR THE RIGHT MEMBER?
-12
,GOOD, YOU SEEM TO UNDERSTAND THIS WORK.
NO, 15+-27=-12
0<  WE HAVE NOW SOLVED THE EQUATION X+27=15 AND FOUND THAT
<X=-12 MAKES THE STATEMENT TRUE.  (TO CHECK; -12+27=15).
.YOU CAN NOW TRY SOME PROBLEMS ON YOUR OWN.
4  REMEMBER THE STEPS IN SOLVING THESE EQUATIONS.
>   1. DETERMINE WHICH VALUE IS ADDED TO X IN THE ORIGINAL
EQUATION.
4   2. FIND THE ADDITIVE INVERSE OF THIS NUMBER.
B   3. ADD THIS ADDITIVE INVERSE TO BOTH SIDES OF THE EQUATION.
   4. CHECK YOUR ANSWER.
  
               GOOD LUCK!
(ARE YOU READY TO TRY SOME PROBLEMS?
(TYPE YES OR NO).
YES
HERE WE GO
ALGE02NO
"OH, LET'S TRY A FEW EASY ONES.
ALGE02TYPE YES OR NO.
N.
4  REMEMBER THE STEPS IN SOLVING THESE EQUATIONS.
>   1. DETERMINE WHICH VALUE IS ADDED TO X IN THE ORIGINAL
EQUATION.
4   2. FIND THE ADDITIVE INVERSE OF THIS NUMBER.
B   3. ADD THIS ADDITIVE INVERS