Algebraic Equation
Linear Equation In One Variable
Equations Reducible To Simpler Form
Solving Linear Equation In One Variable
Linear Equations in One Variable
An algebraic equation with only one type of variable.
Equations of type =
are not linear equations but can be reduced by cross-multiplication
These type of equations can be solved by either of the two methods mentionedearlier.
= 4—44x—4
² 4x + 5 = 9 ; write the equation
² 4x + 5 - 5 = 9 - 5 ; Subtracting 5 on both sides, hence not disturbing the balance.² 4x = 4 ; Simplifying
² x = 1 ; Simplifying
; Dividing by 4 on both sides,hence not disturbing the balance
Type 1 : Variable on one side and number on the other side. For e.g. 4x + 5 = 9
In this method the numbers are moved from one side of equality to other sideby changing the sign. The changes are as follows,
Balancing Method
1
2
3
It is an equality involving variablesFor e.g.
The value of the variable which satis�es the equation is its solution
4x + 5 = 3x - 2
Left Hand Side(LHS) Right Hand Side(RHS)Equality
1
+ changes to -- changes to +% changes to '' changes to %
i
ii
iii
iv
a
a
The rules of transposing numbers are also applicable for variablesb
Transposing Methodb
Type 2 : Variables and numbers on both sides. For e.g. 2x - 3 = x + 22
For e.g.4x + 5 = 9
Taking 5 to RHS4x = 9 - 5
4x = 4Taking 4 to RHS
x = 4—4x = 1
For e.g.2x - 3 = x + 2
Taking 3 to RHS2x = x + 2 + 3
2x = x + 5Taking x to LHS
2x - x = 5x = 5
2( 4x + 3 ) = 3( 3x + 7 )8x + 6 = 9x + 21
And this can be further sorted by transposition
8x = 9x + 21 - 6 8x = 9x +15-15 = 9x - 8x
x = -15
4x + 33x + 7
3—2
4x + 33x + 7
3—2