Lecture notes

Linear Equations
-
Def : An equation of form a ✗ 1-6=0 is a linear equation
the
1 where at 6 are real nbs)
>
In order to solve such equations for ✗ we make use
2 facts
of the following .




then Atc = Btc ( for
any C)
1 If A =3
,

2 If A=B , then A. C B. C lfor C zero)
any non
=
-




X we perform the opposite operations from
" "
•
To isolate
the in the equation
operations
e
.


r




operation opposite operation
1- -




÷
Generally work outwards
,

•
in towards the ✗
( In T
C 12 ✓

Eg : -
Solve for ✗ : 2×-5=0 s


*
Get rid of -5
by doing the 2×-51-5=01-5
opposite operation to both sides : adds 211=5 g
Get rid of -21 multiplication) by ÷ 2 2£ =3 ✗= a
-
Solve -51×-2) 3×1-8 -




5×-1--0=3×1-8
5×-34=81-10
2✗ = 18
✗ = 9
of 3 consecutive is 66 Find the
-
The sum even
integers .

integers
=
Let ✗ = the first integer
then
integer
Explanation
✗+2 = the second
& ✗+4 = the third integer
j

✗ ✗+1×+2×+3×+4


i £ 's 4 's to

, }
We have ✗ 1- ( ✗ + 2) 1-1×1-41=66
3×1-6=66 The
integers are

34=66-6 ✗= 20
311=60 ✗ +2=22
✗ = 20 & ✗+4=24
* Exercises :

i solve for ✗ 2 find the nb such that five
a. 3×-7 =
-

✗ 1- 29 times three more than itself is
b- 51×-21=10 -
( ✗ + 2)
eighty .




C. 3 ✗ § =L -




3 The sum of 2 consecutive odd integers is 72 .
What are
the integers ?
I a.3×-7 = ✗ -

1- 29
3×1-4=291-7
UX 36 =


✗ = 9
b- 51×-21=10 -
( ✗ 1- 2)
5×-10=10 X 2 - -




5kt ✗ = 101-10-2
6 ✗ = 18
✗ =3

Q
Igt §
3
§ 3- §
c. X - = = ✗ = =


5 g
8
✗ =


}
=

§ § § . = = 2