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