Module 1 3 .
Solving Equations :
An equation is an
equivalence between two mathematical expressions
"
involving numbers represented by the equal sign" ,
=
Example : 5+ 3 = 8 24 3 72 .
=
3x + 2: 8 , 9t 3+ + 3 , etc
=
,
.
,
A solution is an value of "X" for which the equation holds true.
Example Verify that
: X= 2 is a solution to 3x + 2 =
.
8
set x=2
:
3(2) + 2 =
8 > 4+ z - = 8/
Example :
what about the solution of X +2= x + 3 ) = X+ 2
so value of "X" Works
any
How to solve an equation?
We need two principles.
1) Distributive Law
ex let a b
, c be number
·
,
a(b +x) = a -
b + a .
c =
(b + c)a
Example :
1(x+5) =
2x + 7 5 . :
2x + 10
2) Equivalence Law
If a +b = c
,
then +C = b+C ,
If a=b
,
the a -c = b -
c .
Example : X-2 = 8 > X - -
1+ 2 = 8 + 2 -> X =
10 .
2x = 4 -
> 5 .
2x =
t .
4 > X
- =
2 .
Solve the following.
a) 3x 4t 3x 6-2 >
3 =
+ 2 =
+ 2 -2 =
- - X
, b) z(x 3) - =
14
>
x=3 = = X 10
-
= .
2
Two equations ax = b and ex =d
.
are said to be equivalent if they have the same solutions.
Example :
We have X goats . We see 8 paws and y horns.
write equation.
2x =4 4x 8 =
horns legs
Example :
Check if they are equivalent
.
a) 3x 21 = and X +4 :
11
: X+ T
X = 11 -
4 = 7 - X =
7 v
b) 12-X 3 = and 2x = 20
V
-
1)-
X =
3 -
12) X =
20/2 = 10
X= d
# X = 18
not equivalent
Solving Equations :
An equation is an
equivalence between two mathematical expressions
"
involving numbers represented by the equal sign" ,
=
Example : 5+ 3 = 8 24 3 72 .
=
3x + 2: 8 , 9t 3+ + 3 , etc
=
,
.
,
A solution is an value of "X" for which the equation holds true.
Example Verify that
: X= 2 is a solution to 3x + 2 =
.
8
set x=2
:
3(2) + 2 =
8 > 4+ z - = 8/
Example :
what about the solution of X +2= x + 3 ) = X+ 2
so value of "X" Works
any
How to solve an equation?
We need two principles.
1) Distributive Law
ex let a b
, c be number
·
,
a(b +x) = a -
b + a .
c =
(b + c)a
Example :
1(x+5) =
2x + 7 5 . :
2x + 10
2) Equivalence Law
If a +b = c
,
then +C = b+C ,
If a=b
,
the a -c = b -
c .
Example : X-2 = 8 > X - -
1+ 2 = 8 + 2 -> X =
10 .
2x = 4 -
> 5 .
2x =
t .
4 > X
- =
2 .
Solve the following.
a) 3x 4t 3x 6-2 >
3 =
+ 2 =
+ 2 -2 =
- - X
, b) z(x 3) - =
14
>
x=3 = = X 10
-
= .
2
Two equations ax = b and ex =d
.
are said to be equivalent if they have the same solutions.
Example :
We have X goats . We see 8 paws and y horns.
write equation.
2x =4 4x 8 =
horns legs
Example :
Check if they are equivalent
.
a) 3x 21 = and X +4 :
11
: X+ T
X = 11 -
4 = 7 - X =
7 v
b) 12-X 3 = and 2x = 20
V
-
1)-
X =
3 -
12) X =
20/2 = 10
X= d
# X = 18
not equivalent
